Relevant bibliographies by topics / Finite difference method of analysis

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  2. Dissertations / Theses
  3. Books
  4. Book chapters
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Academic literature on the topic 'Finite difference method of analysis'

Author: Grafiati
Published: 4 June 2021
Last updated: 7 February 2022

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Journal articles on the topic "Finite difference method of analysis"

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Tang, Hui, Xiao Jun Li, Guo Liang Zhou, and Chun Ming Zhang. "Finite/Explicit Finite Element - Finite Difference Coupling Method for Analysis of Soil - Foundation System." Advanced Materials Research 838-841 (November 2013): 913–17. http://dx.doi.org/10.4028/www.scientific.net/amr.838-841.913.

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There are some coupling methods based on Finite Element Method and some other numerical methods, such as Infinite Element Method, Boundary Element Method, Finite Difference Method, etc. But these methods have their own limitations on simulation the foundation. For overcome these disadvantages, a coupling method is presented in this paper, which be proposed to analyze the effect of soil - foundation on seismic response of structures. In this coupling method, the structure and the surrounding soil are simulated with Finite Element method, and the other part of the soil with Explicit Finite Element - Finite Difference Method. Compared to other coupling methods, it is more flexible and its calculation amount is acceptable. The accuracy and effectiveness of the coupling method have been verified through Numerical experiment in this paper.
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Dow, John O., Michael S. Jones, and Shawn A. Harwood. "A generalized finite difference method for solid mechanics." Numerical Methods for Partial Differential Equations 6, no. 2 (1990): 137–52. http://dx.doi.org/10.1002/num.1690060204.

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Dow, John O., and Ian Stevenson. "Adaptive refinement procedure for the finite difference method." Numerical Methods for Partial Differential Equations 8, no. 6 (November 1992): 537–50. http://dx.doi.org/10.1002/num.1690080604.

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ISHIKAWA, Mikihito, Toshihito OHMI, A. Toshimitsu YOKOBORI Jr., and Masaaki NISHIMURA. "OS1010 The Hydrogen Diffusion Analysis by Finite Element Method and Finite Difference Method." Proceedings of the Materials and Mechanics Conference 2014 (2014): _OS1010–1_—_OS1010–3_. http://dx.doi.org/10.1299/jsmemm.2014._os1010-1_.

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Gupta, Dr A. R. "Comparative analysis of Rectangular Plate by Finite element method and Finite Difference Method." International Journal for Research in Applied Science and Engineering Technology 9, no. 9 (September 30, 2021): 1399–402. http://dx.doi.org/10.22214/ijraset.2021.38153.

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Abstract: Analysis of rectangular plates is common when designing the foundation of civil, traffic, and irrigation works. The current research presents the results of the analysis of rectangular plates using the finite difference method and Finite Element Method. The results of the research verify the accuracy of the FEM and are in agreement with findings in the literature. The plate is analyzed considering it to be completely solid. The ordinary finite difference method is used to solve the governing differential equation of the plate deflection. The proposed method can be easily programmed to readily apply on a plate problem. The work covers the determination of displacement components at different points of the plate and checking the result by software (STAAD.Pro) analysis. Keywords: rectangular plate, FEM, Finite Difference Method
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Gupta, Dr A. R. "Comparative analysis of Rectangular Plate by Finite element method and Finite Difference Method." International Journal for Research in Applied Science and Engineering Technology 9, no. 9 (September 30, 2021): 1397–98. http://dx.doi.org/10.22214/ijraset.2021.38152.

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Abstract: Plates are commonly used to support lateral or vertical loads. Before the design of such a plate, analysis is performed to check the stability of plate for the proposed load. There are several methods for this analysis. In this research, a comparative analysis of rectangular plate is done between Finite Element Method (FEM) and Finite Difference Method (FDM). The plate is considered to be subjected to an arbitrary transverse uniformly distributed loading and is considered to be clamped at the two opposite edges and free at the other two edges. The Finite Element Method (FEM) is a numerical technique for finding approximate solutions to boundary value problems for partial differential equations. It is also referred to as finite element analysis (FEA). FEM subdivides a large problem into smaller, simpler, parts, called finite elements. The work covers the determination of displacement components at different points of the plate and checking the result by software (STAAD.Pro) analysis. The ordinary Finite Difference Method (FDM) is used to solve the governing differential equation of the plate deflection. The proposed methods can be easily programmed to readily apply on a plate problem. Keywords: Arbitrary, FEM, FDM, boundary.
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Ashyralyyev, Charyyar, Ayfer Dural, and Yasar Sozen. "Finite Difference Method for the Reverse Parabolic Problem." Abstract and Applied Analysis 2012 (2012): 1–17. http://dx.doi.org/10.1155/2012/294154.

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A finite difference method for the approximate solution of the reverse multidimensional parabolic differential equation with a multipoint boundary condition and Dirichlet condition is applied. Stability, almost coercive stability, and coercive stability estimates for the solution of the first and second orders of accuracy difference schemes are obtained. The theoretical statements are supported by the numerical example.
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Yang, Dongquan, M. K. Rahman, and Yibai Chen. "Bottomhole assembly analysis by finite difference differential method." International Journal for Numerical Methods in Engineering 74, no. 9 (2008): 1495–517. http://dx.doi.org/10.1002/nme.2221.

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Virdi, Kuldeep S. "Finite difference method for nonlinear analysis of structures." Journal of Constructional Steel Research 62, no. 11 (November 2006): 1210–18. http://dx.doi.org/10.1016/j.jcsr.2006.06.015.

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Tang, X. W., and X. W. Zhang. "Seismic liquefaction analysis by a modified finite element-finite difference method." Japanese Geotechnical Society Special Publication 2, no. 33 (2016): 1204–7. http://dx.doi.org/10.3208/jgssp.chn-58.

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Dissertations / Theses on the topic "Finite difference method of analysis"

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Lidgate, Simon. "Advanced finite difference - beam propagation : method analysis of complex components." Thesis, University of Nottingham, 2004. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.408596.

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Basson, Gysbert. "An explicit finite difference method for analyzing hazardous rock mass." Thesis, Stellenbosch : Stellenbosch University, 2011. http://hdl.handle.net/10019.1/17957.

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Thesis (MSc)--Stellenbosch University, 2011.
ENGLISH ABSTRACT: FLAC3D is a three-dimensional explicit nite difference program for solving a variety of solid mechanics problems, both linear and non-linear. The development of the algorithm and its initial implementation were performed by Itasca Consulting Group Inc. The main idea of the algorithm is to discritise the domain of interest into a Lagrangian grid where each cell represents an element of the material. Each cell can then deform according to a prescribed stress/strain law together with the equations of motion. An in-depth study of the algorithm was performed and implemented in Java. During the implementation, it was observed that the type of boundary conditions typically used has a major in uence on the accuracy of the results, especially when boundaries are close to regions with large stress variations, such as in mining excavations. To improve the accuracy of the algorithm, a new type of boundary condition was developed where the FLAC3D domain is embedded in a linear elastic material, named the Boundary Node Shell (BNS). Using the BNS shows a signi cant improvement in results close to excavations. The FLAC algorithm is also quite amendable to paralellization and a multi-threaded version that makes use of multiple Central Processing Unit (CPU) cores was developed to optimize the speed of the algorithm. The nal outcome is new non-commercial Java source code (JFLAC) which includes the Boundary Node Shell (BNS) and shared memory parallelism over and above the basic FLAC3D algorithm.
AFRIKAANSE OPSOMMING: FLAC3D is 'n eksplisiete eindige verskil program wat 'n verskeidenheid liniêre en nieliniêre soliede meganika probleme kan oplos. Die oorspronklike algoritme en die implimentasies daarvan was deur Itasca Consulting Group Inc. toegepas. Die hoo dee van die algoritme is om 'n gebied te diskritiseer deur gebruik te maak van 'n Lagrangese rooster, waar elke sel van die rooster 'n element van die rooster materiaal beskryf. Elke sel kan dan vervorm volgens 'n sekere spannings/vervormings wet. 'n Indiepte ondersoek van die algoritme was uitgevoer en in Java geïmplimenteer. Tydens die implementering was dit waargeneem dat die grense van die rooster 'n groot invloed het op die akkuraatheid van die resultate. Dit het veral voorgekom in areas waar stress konsentrasies hoog is, gewoonlik naby areas waar myn uitgrawings gemaak is. Dit het die ontwikkelling van 'n nuwe tipe rand kondisie tot gevolg gehad, sodat die akkuraatheid van die resultate kon verbeter. Die nuwe rand kondisie, genaamd die Grens Node Omhulsel (GNO), aanvaar dat die gebied omring is deur 'n elastiese materiaal, wat veroorsaak dat die grense van die gebied 'n elastiese reaksie het op die stress binne die gebied. Die GNO het 'n aansienlike verbetering in die resultate getoon, veral in areas naby myn uitgrawings. Daar was ook waargeneem dat die FLAC algoritme parralleliseerbaar is en het gelei tot die implentering van 'n multi-SVE weergawe van die sagteware om die spoed van die algoritme te optimeer. Die nale uitkomste is 'n nuwe nie-kommersiële Java weergawe van die algoritme (JFLAC), wat die implimentering van die nuwe GNO randwaardekondisie insluit, asook toelaat vir die gebruik van multi- Sentrale Verwerkings Eenheid (SVE) as 'n verbetering op die basiese FLAC3D algoritme.
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Meagher, Timothy P. "A New Finite Difference Time Domain Method to Solve Maxwell's Equations." PDXScholar, 2018. https://pdxscholar.library.pdx.edu/open_access_etds/4389.

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We have constructed a new finite-difference time-domain (FDTD) method in this project. Our new algorithm focuses on the most important and more challenging transverse electric (TE) case. In this case, the electric field is discontinuous across the interface between different dielectric media. We use an electric permittivity that stays as a constant in each medium, and magnetic permittivity that is constant in the whole domain. To handle the interface between different media, we introduce new effective permittivities that incorporates electromagnetic fields boundary conditions. That is, across the interface between two different media, the tangential component, Er(x,y), of the electric field and the normal component, Dn(x,y), of the electric displacement are continuous. Meanwhile, the magnetic field, H(x,y), stays as continuous in the whole domain. Our new algorithm is built based upon the integral version of the Maxwell's equations as well as the above continuity conditions. The theoretical analysis shows that the new algorithm can reach second-order convergence O(∆x2)with mesh size ∆x. The subsequent numerical results demonstrate this algorithm is very stable and its convergence order can reach very close to second order, considering accumulation of some unexpected numerical approximation and truncation errors. In fact, our algorithm has clearly demonstrated significant improvement over all related FDTD methods using effective permittivities reported in the literature. Therefore, our new algorithm turns out to be the most effective and stable FDTD method to solve Maxwell's equations involving multiple media.
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Cai, Ming. "Finite difference time domain method and its application in antenna analysis." Thesis, London South Bank University, 1998. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.263739.

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Garg, Nimisha. "Analysis of Slot Antennas Using the Finite Difference Time Domain Method." FIU Digital Commons, 2001. https://digitalcommons.fiu.edu/etd/3843.

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The objective of this thesis was to analyze a Coplanar Waveguide (CPW)-fed folded slot antenna using the Finite Difference Time Domain (FDTD) method. Important parameters such as S-parameters and the input impedance of the antenna were simulated using XFDTD software and were analyzed. An important goal of this thesis was to provide design information about the folded slot antenna. For this purpose the effects of antenna layout on the resonant frequency and the bandwidth of the antenna were investigated. First the effect of adding more number of slots to the basic CPW-fed folded slot antenna geometry on the S-parameters, the input impedance and the radiation patterns of the antenna were studied. Next the width of the slot was varied and the effect of changing this design parameter of the antenna was analyzed. Finally the slot separation was varied and its effect on the antenna parameters is studied. This work concluded that, by including additional slots, the input impedance of the antenna can be controlled over a wide range.
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Ezertas, Ahmet Alper. "Sensitivity Analysis Using Finite Difference And Analytical Jacobians." Master's thesis, METU, 2009. http://etd.lib.metu.edu.tr/upload/12611067/index.pdf.

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The Flux Jacobian matrices, the elements of which are the derivatives of the flux vectors with respect to the flow variables, are needed to be evaluated in implicit flow solutions and in analytical sensitivity analyzing methods. The main motivation behind this thesis study is to explore the accuracy of the numerically evaluated flux Jacobian matrices and the effects of the errors in those matrices on the convergence of the flow solver, on the accuracy of the sensitivities and on the performance of the design optimization cycle. To perform these objectives a flow solver, which uses exact Newton&rsquo
s method with direct sparse matrix solution technique, is developed for the Euler flow equations. Flux Jacobian is evaluated both numerically and analytically for different upwind flux discretization schemes with second order MUSCL face interpolation. Numerical flux Jacobian matrices that are derived with wide range of finite difference perturbation magnitudes were compared with analytically derived ones and the optimum perturbation magnitude, which minimizes the error in the numerical evaluation, is searched. The factors that impede the accuracy are analyzed and a simple formulation for optimum perturbation magnitude is derived. The sensitivity derivatives are evaluated by direct-differentiation method with discrete approach. The reuse of the LU factors of the flux Jacobian that are evaluated in the flow solution enabled efficient sensitivity analysis. The sensitivities calculated by the analytical Jacobian are compared with the ones that are calculated by numerically evaluated Jacobian matrices. Both internal and external flow problems with varying flow speeds, varying grid types and sizes are solved with different discretization schemes. In these problems, when the optimum perturbation magnitude is used for numerical Jacobian evaluation, the errors in Jacobian matrix and the sensitivities are minimized. Finally, the effect of the accuracy of the sensitivities on the design optimization cycle is analyzed for an inverse airfoil design performed with least squares minimization.
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Roth, Jacob M. "The Explicit Finite Difference Method: Option Pricing Under Stochastic Volatility." Scholarship @ Claremont, 2013. http://scholarship.claremont.edu/cmc_theses/545.

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This paper provides an overview of the finite difference method and its application to approximating financial partial differential equations (PDEs) in incomplete markets. In particular, we study German’s [6] stochastic volatility PDE derived from indifference pricing. In [6], it is shown that the first order- correction to derivatives valued by indifference pricing can be computed as a function involving the stochastic volatility PDE itself. In this paper, we present three explicit finite difference models to approximate the stochastic volatility PDE and compare the resulting valuations to those generated by an Euler- Maruyama Monte Carlo pricing algorithm. We also discuss the significance of boundary condition choice for explicit finite difference models.
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Egorova, Vera. "Finite Difference Methods for nonlinear American Option Pricing models: Numerical Analysis and Computing." Doctoral thesis, Universitat Politècnica de València, 2016. http://hdl.handle.net/10251/68501.

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[EN] The present PhD thesis is focused on numerical analysis and computing of finite difference schemes for several relevant option pricing models that generalize the Black-Scholes model. A careful analysis of desirable properties for the numerical solutions of option pricing models as the positivity, stability and consistency, is provided. In order to handle the free boundary that arises in American option pricing problems, various transformation techniques based on front-fixing method are applied and studied. Special attention is paid to multi-asset option pricing, such as exchange or spread option. Appropriate transformation allows eliminating of the cross derivative term. Transformation techniques of partial differential equations to remove convection and reaction terms are studied in order to simplify the models and avoid possible troubles of stability. This thesis consists of six chapters. The first chapter is an introduction containing definitions of option and related terms and derivation of the Black-Scholes equation as well as general aspects of theory of finite difference schemes, including preliminaries on numerical analysis. Chapter 2 is devoted to solve linear Black-Scholes model for American put and call options. A Landau transformation and a new front-fixing transformation are applied to the free boundary value problem. It leads to non-linear partial differential equation (PDE) in a fixed domain. Stable and consistent explicit numerical schemes are proposed preserving positivity and monotonicity of the solution in accordance with the behaviour of the exact solution. Efficiency of the front-fixing method demonstrated in Chapter 2 has motivated us to apply the method to some more complicated nonlinear models. A new change of variables resulting in a time dependent boundary instead of fixed one, is applied to nonlinear Black-Scholes model for American options, such as Barles and Soner and Risk Adjusted Pricing models. Chapter 4 provides a new alternative approach for solving American option pricing problem based on rationality of investor. There exists an intensity function that can be reduced in the simplest case to penalty approach. Chapter 5 deals with multi-asset option pricing. Appropriate transformation allows eliminating of the cross derivative term avoiding computational drawbacks and possible troubles of stability. Concluding remarks are given in Chapter 6. All the considered models and numerical methods are accompanied by several examples and simulations. The convergence rate is computed confirming the theoretical study of consistency. Stability conditions are tested by numerical examples. Results are compared with known relevant methods in the literature showing efficiency of the proposed methods.
[ES] La presente tesis doctoral se centra en la construcción de esquemas en diferencias finitas y el análisis numérico de relevantes modelos de valoración de opciones que generalizan el modelo de Black-Scholes. Se proporciona un análisis cuidadoso de las propiedades de las soluciones numéricas tales como la positividad, la estabilidad y la consistencia. Con el fin de manejar la frontera libre que surge en los problemas de valoración de opciones Americanas, se aplican y se estudian diversas técnicas de transformación basadas en el método de fijación de las fronteras (front-fixing). Se presta especial atención a la valoración de opciones de múltiples activos, como son las opciones ''exchange'' y ''spread''. Esta tesis se compone de seis capítulos. El primer capítulo es una introducción que contiene las definiciones de opción y términos relacionados y la derivación de la ecuación de Black-Scholes, así como aspectos generales de la teoría de los esquemas en diferencias finitas, incluyendo preliminares de análisis numérico. El capítulo 2 está dedicado a resolver el modelo lineal de Black-Scholes para opciones Americanas put y call. Para fijar las fronteras del problema de frontera libre se aplican transformaciones como la de Landau y un nuevo cambio de variable propuesto. La eficiencia del método front-fixing mostrada en el capítulo 2 ha motivado el estudio de su aplicación a algunos modelos no lineales más complicados. En particular, se propone un cambio de variables que lleva a una nueva frontera dependiente del tiempo en lugar de una fija. Este cambio se aplica a modelos no lineales de Black-Scholes para opciones Americanas, como son el de Barles y Soner y el modelo RAPM (Risk Adjusted Pricing Methodology). El capítulo 4 ofrece una nueva técnica para la resolución de problemas de valoración de opciones Americanas basada en la racionalidad de los inversores. Aparece una función de la intensidad que se puede reducir en el caso más simple a la técnica de penalización (penalty method). Este enfoque tiene en cuenta el posible comportamiento irracional de los inversores. En la sección 4.2 se aplica esta técnica al modelo de cambio de regímenes lo que lleva a un nuevo modelo que tiene en cuenta el posible ejercicio irracional, así como varios estados del mercado. El enfoque del parámetro de racionalidad junto con una transformación logarítmica permiten construir un esquema numérico eficiente sin aplicar el método front-fixing o la conocida formulación de LCP (Linear Complementarity Problem). El capítulo 5 se dedica a la valoración de opciones de activos múltiples. Una transformación apropiada permite la eliminación del término de derivadas cruzadas evitando inconvenientes computacionales y posibles problemas de estabilidad. Las conclusiones se muestran en el capítulo 6. Se pone en relieve varios aspectos de la presente tesis. Todos los modelos considerados y los métodos numéricos van acompañados de varios ejemplos y simulaciones. Se estudia la convergencia numérica que confirma el estudio teórico de la consistencia. Las condiciones de estabilidad son corroboradas con ejemplos numéricos. Los resultados se comparan con métodos relevantes de la bibliografía mostrando la eficiencia de los métodos propuestos.
[CAT] La present tesi doctoral se centra en la construcció d'esquemes en diferències finites i l'anàlisi numèrica de rellevants models de valoració d'opcions que generalitzen el model de Black-Scholes. Es proporciona una anàlisi cuidadosa de les propietats de les solucions numèri-ques com ara la positivitat, l'estabilitat i la consistència. A fi de manejar la frontera lliure que sorgix en els problemes de valoració d'opcions Americanes, s'apliquen i s'estudien diverses tècniques de transformació basades en el mètode de fixació de les fronteres (front-fixing). Es presta especial atenció a la valoració d'opcions de múltiples actius, com són les opcions ''exchange'' i ''spread''. Esta tesi es compon de sis capítols. El primer capítol és una introducció que conté les definicions d'opció i termes relacionats i la derivació de l'equació de Black-Scholes, així com aspectes generals de la teoria dels esquemes en diferències finites, incloent aspectes preliminars d'anàlisi numèrica. El 2n capítol està dedicat a resoldre el model lineal de Black-Scholes per a opcions Americanes ''put'' i ''call''. Per a fixar les fronteres del problema de frontera lliure s'apliquen transformacions com la de Landau i s'ha proposat un nou canvi de variable proposat. Açò porta a una equació diferencial en derivades parcials no lineal en un domini fix. L'eficiència del mètode front-fixing mostrada en el 2n capítol ha motivat l'estudi de la seua aplicació a alguns models no lineals més complicats. En particular, es proposa un canvi de variables que porta a una nova frontera dependent del temps en compte d'una fixa. Este canvi s'aplica a models no lineals de Black-Scholes per a opcions Americanes, com són el de Barles i Soner i el model RAPM (Risk Adjusted Pricing Methodology). El 4t capítol oferix una nova tècnica per a la resolució de problemes de valoració d'opcions Americanes basada en la racionalitat dels inversors. Apareix una funció de la intensitat que es pot reduir en el cas més simple a la tècnica de penalització (penal method) . Este enfocament té en compte el possible comportament irracional dels inversors. En la secció 4.2 s'aplica esta tècnica al model de canvi de règims el que porta a un nou model que té en compte el possible exercici irracional, així com diversos estats del mercat. L'enfocament del paràmetre de racionalitat junt amb una transformació logarítmica permeten construir un esquema numèric eficient sense aplicar el mètode front-fixing o la coneguda formulació de LCP (Linear Complementarity Problem). El 5é capítol es dedica a la valoració d'opcions d'actius múltiples. Una transformació apropiada permet l'eliminació del terme de derivades mixtes evitant inconvenients computacionals i possibles problemes d' estabilitat. Les conclusions es mostren al 6é capítol. Es posa en relleu diversos aspectes de la present tesi. Tots els models considerats i els mètodes numèrics van acompanyats de diversos exemples i simulacions. S'estu-dia la convergència numèrica que confirma l'estudi teòric de la consistència. Les condicions d'estabilitat són corroborades amb exemples numèrics. Els resultats es comparen amb mètodes rellevants de la bibliografia mostrant l'eficiència dels mètodes proposats.
Egorova, V. (2016). Finite Difference Methods for nonlinear American Option Pricing models: Numerical Analysis and Computing [Tesis doctoral no publicada]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/68501
TESIS
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Turan, Umut. "Simulation Of A Batch Dryer By The Finite Difference Method." Master's thesis, METU, 2005. http://etd.lib.metu.edu.tr/upload/12606478/index.pdf.

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The objectives of this study are to investigate the dynamic behavior of an apple slab subjected to drying at constant external conditions and under changing in the drying temperatures and to determine the effects of temperature and time combinations at different steps during drying on the process dynamics parameters, time constant and process gain of the system. For this purpose, a semi-batch dryer system was simulated by using integral method of analysis. Initially, the dynamic behavior of the drying temperature was investigated by using first order system dynamic model. Process dynamic parameters, time constant and process gain of the system, for change in drying temperature were determined. Secondly, investigation of the drying kinetics of the apple slab was carried out under constant external conditions in a semi-batch dryer. A mathematical model for diffusion mechanism assumed in one dimensional transient analysis of moisture distribution was solved by using explicit finite difference method of analysis. Thirdly, investigation of the drying kinetics of the apple slab was carried out under change in drying temperature at different time steps during drying. Inverse response system model was used for the representation of the dynamic behavior of drying. Process dynamic parameters, time constant and process gain of the system were determined. Model predicted results for apple slab drying under constant external condition and under step change in the drying temperature were compared with the experimental data.
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Wang, Siyang. "Finite Difference and Discontinuous Galerkin Methods for Wave Equations." Doctoral thesis, Uppsala universitet, Avdelningen för beräkningsvetenskap, 2017. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-320614.

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Wave propagation problems can be modeled by partial differential equations. In this thesis, we study wave propagation in fluids and in solids, modeled by the acoustic wave equation and the elastic wave equation, respectively. In real-world applications, waves often propagate in heterogeneous media with complex geometries, which makes it impossible to derive exact solutions to the governing equations. Alternatively, we seek approximated solutions by constructing numerical methods and implementing on modern computers. An efficient numerical method produces accurate approximations at low computational cost. There are many choices of numerical methods for solving partial differential equations. Which method is more efficient than the others depends on the particular problem we consider. In this thesis, we study two numerical methods: the finite difference method and the discontinuous Galerkin method. The finite difference method is conceptually simple and easy to implement, but has difficulties in handling complex geometries of the computational domain. We construct high order finite difference methods for wave propagation in heterogeneous media with complex geometries. In addition, we derive error estimates to a class of finite difference operators applied to the acoustic wave equation. The discontinuous Galerkin method is flexible with complex geometries. Moreover, the discontinuous nature between elements makes the method suitable for multiphysics problems. We use an energy based discontinuous Galerkin method to solve a coupled acoustic-elastic problem.
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Books on the topic "Finite difference method of analysis"

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J, Luebbers Raymond, ed. The finite difference time domain method for electromagnetics. Boca Raton: CRC Press, 1993.

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Applications of discrete functional analysis to the finite difference method. Beijing: International Academic Publishers, 1991.

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Zhou, Yulin. Applications of discrete functional analysis to the finite difference method. Oxford: International Academic Publishers, 1991.

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Baysal, Oktay. An overlapped grid method for multigrid, finite volume/difference flow solvers - MaGGiE. Hampton, Va: National Aeronautics and Space Administration, Langley Research Center, 1990.

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1946-, Chen Zhongying, and Wu Wei 1929-, eds. Generalized difference methods for differential equations: Numerical analysis of finite volume methods. New York: M. Dekker, 2000.

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Hesthaven, Jan S. A waverlet optimized adaptive multi-domain method. Hampton, Va: National Aeronautics and Space Administration, Langley Research Center, 1997.

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Inan, Umran S. Numerical electromagnetics: The FDTD method. Cambridge: Cambridge University Press, 2011.

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Baker, A. J. Analysis of boundary conditions for SSME subsonic internal viscous flow analysis. Knoxville, TN: Computational Mechanics Corporation, 1986.

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Baker, A. J. Analysis of boundary conditions for SSME subsonic internal viscous flow analysis. Knoxville, TN: Computational Mechanics Corporation, 1986.

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Finlayson, Bruce A. Numerical methods for problems with moving fronts. Seattle, Wash., USA: Ravenna Park Pub., 1992.

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Book chapters on the topic "Finite difference method of analysis"

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Zhou, Pei-bai. "Finite Difference Method." In Numerical Analysis of Electromagnetic Fields, 63–94. Berlin, Heidelberg: Springer Berlin Heidelberg, 1993. http://dx.doi.org/10.1007/978-3-642-50319-1_3.

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Chekmarev, Dmitry T. "Some Results of FEM Schemes Analysis by Finite Difference Method." In Finite Difference Methods,Theory and Applications, 153–60. Cham: Springer International Publishing, 2015. http://dx.doi.org/10.1007/978-3-319-20239-6_14.

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da Veiga, Lourenço Beirão, Konstantin Lipnikov, and Gianmarco Manzini. "Analysis of parameters and maximum principles." In The Mimetic Finite Difference Method for Elliptic Problems, 311–37. Cham: Springer International Publishing, 2014. http://dx.doi.org/10.1007/978-3-319-02663-3_11.

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Csomós, Petra, István Faragó, and Imre Fekete. "Operator Semigroups for Convergence Analysis." In Finite Difference Methods,Theory and Applications, 38–49. Cham: Springer International Publishing, 2015. http://dx.doi.org/10.1007/978-3-319-20239-6_4.

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Patel, Kuldip Singh, and Mani Mehra. "High-Order Compact Finite Difference Method for Black–Scholes PDE." In Mathematical Analysis and its Applications, 393–403. New Delhi: Springer India, 2015. http://dx.doi.org/10.1007/978-81-322-2485-3_32.

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Kachalov, Vasiliy I. "Analytic Theory of Singular Perturbations and Lomov’s Regularization Method." In Finite Difference Methods. Theory and Applications, 305–12. Cham: Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-11539-5_34.

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Company, Rafael, Vera N. Egorova, Mohamed El Fakharany, Lucas Jódar, and Fazlollah Soleymani. "Numerical Analysis of Novel Finite Difference Methods." In Novel Methods in Computational Finance, 171–214. Cham: Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-61282-9_10.

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Khawaja, Hassan A. "Solution of Pure Scattering Radiation Transport Equation (RTE) Using Finite Difference Method (FDM)." In Image Analysis, 492–501. Cham: Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-59126-1_41.

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Achdou, Yves. "Finite Difference Methods for Mean Field Games." In Hamilton-Jacobi Equations: Approximations, Numerical Analysis and Applications, 1–47. Berlin, Heidelberg: Springer Berlin Heidelberg, 2013. http://dx.doi.org/10.1007/978-3-642-36433-4_1.

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Zhao, Z. "A Modified Finite Difference Method to Shape Design Sensitivity Analysis." In Boundary Elements XIII, 755–65. Dordrecht: Springer Netherlands, 1991. http://dx.doi.org/10.1007/978-94-011-3696-9_60.

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Conference papers on the topic "Finite difference method of analysis"

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Ashyralyev, Allaberen, Deniz Ağirseven, Theodore E. Simos, George Psihoyios, Ch Tsitouras, and Zacharias Anastassi. "Finite Difference Method for Delay Parabolic Equations." In NUMERICAL ANALYSIS AND APPLIED MATHEMATICS ICNAAM 2011: International Conference on Numerical Analysis and Applied Mathematics. AIP, 2011. http://dx.doi.org/10.1063/1.3636795.

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Ashyralyev, Allaberen, Mehmet Emin San, Theodore E. Simos, George Psihoyios, Ch Tsitouras, and Zacharias Anastassi. "Finite Difference Method for Stochastic Parabolic Equations." In NUMERICAL ANALYSIS AND APPLIED MATHEMATICS ICNAAM 2011: International Conference on Numerical Analysis and Applied Mathematics. AIP, 2011. http://dx.doi.org/10.1063/1.3636799.

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Beilina, L., Theodore E. Simos, George Psihoyios, and Ch Tsitouras. "Hybrid Discontinuous Finite Element∕Finite Difference Method for Maxwell’s Equations." In ICNAAM 2010: International Conference of Numerical Analysis and Applied Mathematics 2010. AIP, 2010. http://dx.doi.org/10.1063/1.3498465.

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Barkhudaryan, Rafayel. "Finite difference method for two-phase obstacle problem." In 11TH INTERNATIONAL CONFERENCE OF NUMERICAL ANALYSIS AND APPLIED MATHEMATICS 2013: ICNAAM 2013. AIP, 2013. http://dx.doi.org/10.1063/1.4825987.

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Ibrahimov, Vagif, and Aliyeva Vusala. "The construction of the finite-difference method and application." In PROCEEDINGS OF THE INTERNATIONAL CONFERENCE ON NUMERICAL ANALYSIS AND APPLIED MATHEMATICS 2014 (ICNAAM-2014). AIP Publishing LLC, 2015. http://dx.doi.org/10.1063/1.4913104.

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Abdollahi, Vahid, and Amir Nejat. "Compressible Fluid Flow Simulation Using Finite Difference Lattice Boltzmann Method." In ASME 2010 10th Biennial Conference on Engineering Systems Design and Analysis. ASMEDC, 2010. http://dx.doi.org/10.1115/esda2010-24081.

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Abstract:
A finite difference lattice Boltzmann method (FDLBM) is employed to simulate the compressible inviscid/viscous flows. The robustness of the employed approach is tested for the shock tube or Riemann problem in some distinct cases including strong pressure shock, the stationary contact discontinuity and the weak acoustic wave. The Results are compared with the exact solutions, as well as other classical finite volume CFD techniques (Steger-Warming, Roe and AUSM flux). The validity of the employed LBM approach is studied. This research reveals some of the challenges involved in simulating the compressible flows using FDLBM.
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Tosa, V., Katalin Kovacs, P. Mercea, and O. Piringer. "A Finite Difference Method for Modeling Migration of Impurities in Multilayer Systems." In NUMERICAL ANALYSIS AND APPLIED MATHEMATICS: International Conference on Numerical Analysis and Applied Mathematics 2008. American Institute of Physics, 2008. http://dx.doi.org/10.1063/1.2991052.

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Feng, Qinghua, Theodore E. Simos, George Psihoyios, and Ch Tsitouras. "A Class of Parallel Finite Difference Method for Convection-Diffusion Equations." In NUMERICAL ANALYSIS AND APPLIED MATHEMATICS: International Conference on Numerical Analysis and Applied Mathematics 2009: Volume 1 and Volume 2. AIP, 2009. http://dx.doi.org/10.1063/1.3241422.

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Bao, Wendi, Yongzhong Song, Theodore E. Simos, George Psihoyios, Ch Tsitouras, and Zacharias Anastassi. "A Local RBF-generated Finite Difference Method for Partial Differential Algebraic Equations." In NUMERICAL ANALYSIS AND APPLIED MATHEMATICS ICNAAM 2011: International Conference on Numerical Analysis and Applied Mathematics. AIP, 2011. http://dx.doi.org/10.1063/1.3636968.

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Cook, Chase, Zeyu Sun, Taeyoung Kim, and Sheldon X. D. Tan. "Finite difference method for electromigration analysis of multi-branch interconnects." In 2016 13th International Conference on Synthesis, Modeling, Analysis and Simulation Methods and Applications to Circuit Design (SMACD). IEEE, 2016. http://dx.doi.org/10.1109/smacd.2016.7520752.

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Reports on the topic "Finite difference method of analysis"

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Huff, K. D., and T. H. Bauer. Benchmarking a new closed-form thermal analysis technique against a traditional lumped parameter, finite-difference method. Office of Scientific and Technical Information (OSTI), August 2012. http://dx.doi.org/10.2172/1049041.

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Manzini, Gianmarco. The Mimetic Finite Difference Method. Office of Scientific and Technical Information (OSTI), May 2013. http://dx.doi.org/10.2172/1078363.

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Mughabghab, S., A. Azarm, and D. Stock. Macroscopic traffic modeling with the finite difference method. Office of Scientific and Technical Information (OSTI), March 1996. http://dx.doi.org/10.2172/226027.

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Chen, Guo, Zhilin Li, and Ping Lin. A Fast Finite Difference Method for Biharmonic Equations on Irregular Domains. Fort Belvoir, VA: Defense Technical Information Center, January 2004. http://dx.doi.org/10.21236/ada444064.

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Mei, Kenneth K. Conformal Time Domain Finite Difference Method of Solving Electromagnetic Wave Scattering. Fort Belvoir, VA: Defense Technical Information Center, October 1988. http://dx.doi.org/10.21236/ada200921.

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Meagher, Timothy. A New Finite Difference Time Domain Method to Solve Maxwell's Equations. Portland State University Library, January 2000. http://dx.doi.org/10.15760/etd.6273.

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Naranjo, Sebastian, and Vitaliy Gyrya. A Low Order Mimetic Finite Difference Method for Resistive Magnetohydrodynamics in 2D. Office of Scientific and Technical Information (OSTI), September 2018. http://dx.doi.org/10.2172/1473774.

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Manzini, Gianmarco, Daniil Svyatskiy, Enrico Bertolazzi, and Marco Frego. A non-linear constrained optimization technique for the mimetic finite difference method. Office of Scientific and Technical Information (OSTI), September 2014. http://dx.doi.org/10.2172/1159216.

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Laguna, G. Generating meshes for finite difference analysis using MGED solid models. Office of Scientific and Technical Information (OSTI), April 1989. http://dx.doi.org/10.2172/6235719.

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Shellman, C. H. Use of the Implicit-Finite-Difference Method to Implement the Parabolic Equation Model. Fort Belvoir, VA: Defense Technical Information Center, February 1991. http://dx.doi.org/10.21236/ada237437.

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