Relevant bibliographies by topics / Higher order differential analysis / Dissertations / Theses
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Dissertations / Theses on the topic 'Higher order differential analysis'

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Published: 3 June 2025
Last updated: 31 July 2025

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1

Tjomsland, Mathias Farvolden. "Isogeometric Analysis : Higher-Order Differential Equations." Thesis, Norges teknisk-naturvitenskapelige universitet, Institutt for matematiske fag, 2013. http://urn.kb.se/resolve?urn=urn:nbn:no:ntnu:diva-24137.

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This thesis introduces Isogeometric Analysis as a potentional bridge between the Finite Element Analysis (FEA) and Computer Aided Design (CAD) communities. An introduction to B-splines and B-spline-based Isogeometric Analysis is given. Then an implemented Isogeometric Analysis solver is used to solve both the Poisson problem and the higher order Biharmonic equation on the unit square. The significant convergence results for Isogeometric Analysis is verified in both cases. Lastly, the highly non-linear, and stiff, Cahn-Hilliard equation is studied. The implemented solver is used to show good re
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2

Muller, Jacob. "Higher order differential operators on graphs." Licentiate thesis, Stockholms universitet, Matematiska institutionen, 2020. http://urn.kb.se/resolve?urn=urn:nbn:se:su:diva-178070.

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This thesis consists of two papers, enumerated by Roman numerals. The main focus is on the spectral theory of <img src="http://www.diva-portal.org/cgi-bin/mimetex.cgi?n" />-Laplacians. Here, an <img src="http://www.diva-portal.org/cgi-bin/mimetex.cgi?n" />-Laplacian, for integer <img src="http://www.diva-portal.org/cgi-bin/mimetex.cgi?n" />, refers to a metric graph equipped with a differential operator whose differential expression is the <img src="http://www.diva-portal.org/cgi-bin/mimetex.cgi?2n" />-th derivative. In Paper I, a classification of all vertex conditions corresponding to self-a
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3

Altintan, Derya. "An Extension To The Variational Iteration Method For Systems And Higher-order Differential Equations." Phd thesis, METU, 2011. http://etd.lib.metu.edu.tr/upload/12613864/index.pdf.

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It is obvious that differential equations can be used to model real-life problems. Although it is possible to obtain analytical solutions of some of them, it is in general difficult to find closed form solutions of differential equations. Finding thus approximate solutions has been the subject of many researchers from different areas. In this thesis, we propose a new approach to Variational Iteration Method (VIM) to obtain the solutions of systems of first-order differential equations. The main contribution of the thesis to VIM is that proposed approach uses restricted variations only for the
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4

Bright, Theresa Ann. "New solutions to the euler equations using lie group analysis and high order numerical techniques." Diss., Georgia Institute of Technology, 1993. http://hdl.handle.net/1853/29990.

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5

Ellis, Truman Everett. "High Order Finite Elements for Lagrangian Computational Fluid Dynamics." DigitalCommons@CalPoly, 2010. https://digitalcommons.calpoly.edu/theses/282.

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A general finite element method is presented to solve the Euler equations in a Lagrangian reference frame. This FEM framework allows for separate arbitrarily high order representation of kinematic and thermodynamic variables. An accompanying hydrodynamics code written in Matlab is presented as a test-bed to experiment with various basis function choices. A wide range of basis function pairs are postulated and a few choices are developed further, including the bi-quadratic Q2-Q1d and Q2-Q2d elements. These are compared with a corresponding pair of low order bi-linear elements, traditional Q1-Q0
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6

Dai, Ruxin. "Richardson Extrapolation-Based High Accuracy High Efficiency Computation for Partial Differential Equations." UKnowledge, 2014. http://uknowledge.uky.edu/cs_etds/20.

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In this dissertation, Richardson extrapolation and other computational techniques are used to develop a series of high accuracy high efficiency solution techniques for solving partial differential equations (PDEs). A Richardson extrapolation-based sixth-order method with multiple coarse grid (MCG) updating strategy is developed for 2D and 3D steady-state equations on uniform grids. Richardson extrapolation is applied to explicitly obtain a sixth-order solution on the coarse grid from two fourth-order solutions with different related scale grids. The MCG updating strategy directly computes a si
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7

Heuer, Christof. "High-order compact finite difference schemes for parabolic partial differential equations with mixed derivative terms and applications in computational finance." Thesis, University of Sussex, 2014. http://sro.sussex.ac.uk/id/eprint/49800/.

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This thesis is concerned with the derivation, numerical analysis and implementation of high-order compact finite difference schemes for parabolic partial differential equations in multiple spatial dimensions. All those partial differential equations contain mixed derivative terms. The resulting schemes have been applied to equations appearing in computational finance. First, we develop and study essentially high-order compact finite difference schemes in a general setting with option pricing in stochastic volatility models on non-uniform grids as application. The schemes are fourth-order accur
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8

Arthurs, Christopher J. "Efficient simulation of cardiac electrical propagation using adaptive high-order finite elements." Thesis, University of Oxford, 2013. http://ora.ox.ac.uk/objects/uuid:ad31f06f-c4ed-4c48-b978-1ef3b12fe7a1.

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This thesis investigates the high-order hierarchical finite element method, also known as the finite element p-version, as a computationally-efficient technique for generating numerical solutions to the cardiac monodomain equation. We first present it as a uniform-order method, and through an a priori error bound we explain why the associated cardiac cell model must be thought of as a PDE and approximated to high-order in order to obtain the accuracy that the p-version is capable of. We perform simulations demonstrating that the achieved error agrees very well with the a priori error bound. Fu
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9

Pal, Kamal K. "Higher order numerical methods for fractional order differential equations." Thesis, University of Chester, 2015. http://hdl.handle.net/10034/613354.

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10

Sayi, Mbani T. "High Accuracy Fitted Operator Methods for Solving Interior Layer Problems." University of the Western Cape, 2020. http://hdl.handle.net/11394/7320.

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Philosophiae Doctor - PhD<br>Fitted operator finite difference methods (FOFDMs) for singularly perturbed problems have been explored for the last three decades. The construction of these numerical schemes is based on introducing a fitting factor along with the diffusion coefficient or by using principles of the non-standard finite difference methods. The FOFDMs based on the latter idea, are easy to construct and they are extendible to solve partial differential equations (PDEs) and their systems. Noting this flexible feature of the FOFDMs, this thesis deals with extension of these metho
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11

Grah, Joana Sarah. "Mathematical imaging tools in cancer research : from mitosis analysis to sparse regularisation." Thesis, University of Cambridge, 2018. https://www.repository.cam.ac.uk/handle/1810/273243.

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This dissertation deals with customised image analysis tools in cancer research. In the field of biomedical sciences, mathematical imaging has become crucial in order to account for advancements in technical equipment and data storage by sound mathematical methods that can process and analyse imaging data in an automated way. This thesis contributes to the development of such mathematically sound imaging models in four ways: (i) automated cell segmentation and tracking. In cancer drug development, time-lapse light microscopy experiments are conducted for performance validation. The aim is to m
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12

Cheema, Tasleem Akhter. "Higher-order finite-difference methods for partial differential equations." Thesis, Brunel University, 1997. http://bura.brunel.ac.uk/handle/2438/7131.

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This thesis develops two families of numerical methods, based upon rational approximations having distinct real poles, for solving first- and second-order parabolic/ hyperbolic partial differential equations. These methods are thirdand fourth-order accurate in space and time, and do not require the use of complex arithmetic. In these methods first- and second-order spatial derivatives are approximated by finite-difference approximations which produce systems of ordinary differential equations expressible in vector-matrix forms. Solutions of these systems satisfy recurrence relations which lead
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13

Alhojilan, Yazid Yousef M. "Higher-order numerical scheme for solving stochastic differential equations." Thesis, University of Edinburgh, 2016. http://hdl.handle.net/1842/15973.

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We present a new pathwise approximation method for stochastic differential equations driven by Brownian motion which does not require simulation of the stochastic integrals. The method is developed to give Wasserstein bounds O(h3/2) and O(h2) which are better than the Euler and Milstein strong error rates O(√h) and O(h) respectively, where h is the step-size. It assumes nondegeneracy of the diffusion matrix. We have used the Taylor expansion but generate an approximation to the expansion as a whole rather than generating individual terms. We replace the iterated stochastic integrals in the met
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14

Williams, J. F. "Scaling and singularities in higher-order nonlinear differential equations." Thesis, University of Bath, 2003. https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.275878.

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15

Duke, Elizabeth R. "Solving higher order dynamic equations on time scales as first order systems." Huntington, WV : [Marshall University Libraries], 2006. http://www.marshall.edu/etd/descript.asp?ref=653.

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16

Kubeisa, S., Hassan Ugail, and M. J. Wilson. "Interactive design using higher order PDE's." Springer Berlin, 2004. http://hdl.handle.net/10454/2659.

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Yes<br>This paper extends the PDE method of surface generation. The governing partial differential equation is generalised to sixth order to increase its flexibility. The PDE is solved analytically, even in the case of general boundary conditions, making the method fast. The boundary conditions, which control the surface shape, are specified interactively, allowing intuitive manipulation of generic shapes. A compact user interface is presented which makes use of direct manipulation and other techniques for 3D interaction.
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17

Ugur, Omur. "Boundary Value Problems For Higher Order Linear Impulsive Differential Equations." Phd thesis, METU, 2003. http://etd.lib.metu.edu.tr/upload/686691/index.pdf.

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_I The theory of impulsive di&reg<br>erential equations has become an important area of research in recent years. Linear equations, meanwhile, are fundamental in most branches of applied mathematics, science, and technology. The theory of higher order linear impulsive equations, however, has not been studied as much as the cor- responding theory of ordinary di&reg<br>erential equations. In this work, higher order linear impulsive equations at &macr<br>xed moments of impulses together with certain boundary conditions are investigated by making use of a Green&#039<br>s formula, constructed for p
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18

Taj, Malik Shahadat Ali. "Higher order parallel splitting methods for parabolic partial differential equations." Thesis, Brunel University, 1995. http://bura.brunel.ac.uk/handle/2438/5780.

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The thesis develops two families of numerical methods, based upon new rational approximations to the matrix exponential function, for solving second-order parabolic partial differential equations. These methods are L-stable, third- and fourth-order accurate in space and time, and do not require the use of complex arithmetic. In these methods second-order spatial derivatives are approximated by new difference approximations. Then parallel algorithms are developed and tested on one-, two- and three-dimensional heat equations, with constant coefficients, subject to homogeneous boundary conditions
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19

Honeycutt, Rebecca Lee. "Higher order algorithms for the numerical integration of stochastic differential equations." Diss., Georgia Institute of Technology, 1990. http://hdl.handle.net/1853/29907.

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20

Claire, Narinder Singh. "Spectral theory and heat kernel estimates for higher order differential operators." Thesis, King's College London (University of London), 2000. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.395811.

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21

Might, Matthew Brendon. "Environment Analysis of Higher-Order Languages." Diss., Georgia Institute of Technology, 2007. http://hdl.handle.net/1853/16289.

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Any analysis of higher-order languages must grapple with the tri-facetted nature of lambda. In one construct, the fundamental control, environment and data structures of a language meet and intertwine. With the control facet tamed nearly two decades ago, this work brings the environment facet to heel, defining the environment problem and developing its solution: environment analysis. Environment analysis allows a compiler to reason about the equivalence of environments, i.e., name-to-value mappings, that arise during a program's execution. In this dissertation, two different techniques-abstrac
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22

Andréasson, Fredrik. "Higher order differentials and generalized Cartan-de Rham complexes." Doctoral thesis, KTH, Mathematics, 2003. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-3597.

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23

Du, Zhihua [Verfasser]. "Boundary Value Problems for Higher Order Complex Partial Differential Equations / Zhihua Du." Berlin : Freie Universität Berlin, 2008. http://d-nb.info/1022870912/34.

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24

OKUMURA, Ryuhei, 隆平 奥村, Dapeng CAI, 大鵬 蔡, and Takashi Gyoshin NITTA. "Transversality Conditions for Infinite Horizon Optimality:Higher Order Differential Problems." Elsevier, 2009. http://hdl.handle.net/2237/11356.

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25

Fedosov, Boris, Bert-Wolfgang Schulze, and Nikolai N. Tarkhanov. "The index of higher order operators on singular surfaces." Universität Potsdam, 1998. http://opus.kobv.de/ubp/volltexte/2008/2512/.

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The index formula for elliptic pseudodifferential operators on a two-dimensional manifold with conical points contains the Atiyah-Singer integral as well as two additional terms. One of the two is the 'eta' invariant defined by the conormal symbol, and the other term is explicitly expressed via the principal and subprincipal symbols of the operator at conical points. In the preceding paper we clarified the meaning of the additional terms for first-order differential operators. The aim of this paper is an explicit description of the contribution of a conical point for higher-order differential
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26

Sereni, Damien. "Termination analysis of higher-order functional programs." Thesis, University of Oxford, 2006. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.437001.

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27

Ferone, A. "EXPLOITING HIGHER ORDER UNCERTAINTY IN IMAGE ANALYSIS." Doctoral thesis, Università degli Studi di Milano, 2011. http://hdl.handle.net/2434/155479.

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Soft computing is a group of methodologies that works synergistically to provide flexible information processing capability for handling real-life ambiguous situations. Its aim is to exploit the tolerance for imprecision, uncertainty, approximate reasoning, and partial truth in order to achieve tractability, robustness, and low-cost solutions. Soft computing methodologies (involving fuzzy sets, neural networks, genetic algorithms, and rough sets) have been successfully employed in various image processing tasks including image segmentation, enhancement and classification, both individually or
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28

Smith, James. "Global time estimates for solutions to higher order strictly hyperbolic partial differential equations." Thesis, Imperial College London, 2006. http://hdl.handle.net/10044/1/1267.

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In this thesis we consider the Cauchy problem for general higher order constant coefficient strictly hyperbolic PDEs with lower order terms and show how the behaviour of the characteristic roots determine the rate of decay in the associated Lp-Lq estimates. In particular, we show under what conditions the solution behaves like that of the standard wave equation, the wave equation with dissipation or the Klein-Gordon equation. We explain the various factors involved, such as the presence of multiple roots, the size of the sets of multiplicity and the order with which characteristics meet the re
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29

Chrusch, Peter P. "Conventional and differential scanning optical microscopy using higher-order Gaussian-Hermite beam patterns /." Online version of thesis, 1990. http://hdl.handle.net/1850/10897.

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30

Shi, Chunchao. "Linear differential algebraic equations of higher order and the regularity or singularity of matrix polynomials." [S.l.] : [s.n.], 2004. http://deposit.ddb.de/cgi-bin/dokserv?idn=971887314.

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31

Morrison, Tegan Ann. "Asymptotics of higher-order Painlevé equations." Thesis, The University of Sydney, 2009. http://hdl.handle.net/2123/5140.

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We undertake an asymptotic study of a second Painlevé hierarchy based on the Jimbo-Miwa Lax pair in the limit as the independent variable approaches infinity. The hierarchy is defined by an infinite sequence of non-linear ordinary differential equations, indexed by order, with the classical second Painlevé equation as the first member. We investigate general and special asymptotic behaviours admitted by each equation in the hierarchy. We show that the general asymptotic behaviour is described by two related hyperelliptic functions, where the genus of the functions increases with each member of
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32

Morrison, Tegan Ann. "Asymptotics of higher-order Painlevé equations." University of Sydney, 2009. http://hdl.handle.net/2123/5140.

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Doctor of Philosophy (PhD)<br>We undertake an asymptotic study of a second Painlevé hierarchy based on the Jimbo-Miwa Lax pair in the limit as the independent variable approaches infinity. The hierarchy is defined by an infinite sequence of non-linear ordinary differential equations, indexed by order, with the classical second Painlevé equation as the first member. We investigate general and special asymptotic behaviours admitted by each equation in the hierarchy. We show that the general asymptotic behaviour is described by two related hyperelliptic functions, where the genus of the functions
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33

Mohan, Anuraag. "Higher order transient analysis of composite wire structures." Access to citation, abstract and download form provided by ProQuest Information and Learning Company; downloadable PDF file, 166 p, 2007. http://proquest.umi.com/pqdweb?did=1362532781&sid=43&Fmt=2&clientId=8331&RQT=309&VName=PQD.

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34

Moore, Benjamin Luke. "Unravelling higher order chromatin organisation through statistical analysis." Thesis, University of Edinburgh, 2016. http://hdl.handle.net/1842/22906.

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Recent technological advances underpinned by high throughput sequencing have given new insights into the three-dimensional structure of mammalian genomes. Chromatin conformation assays have been the critical development in this area, particularly the Hi-C method which ascertains genome-wide patterns of intra and inter-chromosomal contacts. However many open questions remain concerning the functional relevance of such higher order structure, the extent to which it varies, and how it relates to other features of the genomic and epigenomic landscape. Current knowledge of nuclear architecture desc
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35

Wu, Tao. "Higher-order Random Walk Methods for Data Analysis." Thesis, Purdue University, 2018. http://pqdtopen.proquest.com/#viewpdf?dispub=10790747.

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<p> Markov random walk models are powerful analytical tools for multiple areas in machine learning, numerical optimizations and data mining tasks. The key assumption of a first-order Markov chain is memorylessness, which restricts the dependence of the transition distribution to the current state only. However in many applications, this assumption is not appropriate. We propose a set of higher-order random walk techniques and discuss their applications to tensor co-clustering, user trails modeling, and solving linear systems. First, we develop a new random walk model that we call the super-spa
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36

Porter, Thomas Louis. "A Higher Order Analysis of Sparse Normal Mixtures." Thesis, The University of Sydney, 2017. http://hdl.handle.net/2123/18002.

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The Donoho and Jin (2004) higher criticism statistic (HC) is an increasingly popular tool in sparse mixture detection, feature selection, and classification problems. We consider the extensively studied sparse normal mixture detection problem, which has been used as a testing ground for other procedures (such as the Jager and Wellner (2007) phi-divergence statistics, of which HC is a particular case). We reveal an alternative interpretation for HC, which perhaps explains some of its strengths and weaknesses in sparse mixture detection. Several implications of this interpretation are establis
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37

Ferrer, Esteban. "A high order Discontinuous Galerkin - Fourier incompressible 3D Navier-Stokes solver with rotating sliding meshes for simulating cross-flow turbines." Thesis, University of Oxford, 2012. http://ora.ox.ac.uk/objects/uuid:db8fe6e3-25d0-4f6a-be1b-6cde7832296d.

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This thesis details the development, verification and validation of an unsteady unstructured high order (≥ 3) h/p Discontinuous Galerkin - Fourier solver for the incompressible Navier-Stokes equations on static and rotating meshes in two and three dimensions. This general purpose solver is used to provide insight into cross-flow (wind or tidal) turbine physical phenomena. Simulation of this type of turbine for renewable energy generation needs to account for the rotational motion of the blades with respect to the fixed environment. This rotational motion implies azimuthal changes in blade aero
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38

Pipilis, Konstantinos Georgiou. "Higher order moving finite element methods for systems described by partial differential-algebraic equations." Thesis, Imperial College London, 1990. http://hdl.handle.net/10044/1/7510.

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39

Temimi, Helmi. "A Discontinuous Galerkin Method for Higher-Order Differential Equations Applied to the Wave Equation." Diss., Virginia Tech, 2008. http://hdl.handle.net/10919/26454.

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We propose a new discontinuous finite element method for higher-order initial value problems where the finite element solution exhibits an optimal convergence rate in the L2- norm. We further show that the q-degree discontinuous solution of a differential equation of order m and its first (m-1)-derivatives are strongly superconvergent at the end of each step. We also establish that the q-degree discontinuous solution is superconvergent at the roots of (q+1-m)-degree Jacobi polynomial on each step. Furthermore, we use these results to construct asymptotically correct a posteriori error estimat
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40

Oskooei, Saeid G. "A higher order finite element for sandwich plate analysis." Thesis, National Library of Canada = Bibliothèque nationale du Canada, 1998. http://www.collectionscanada.ca/obj/s4/f2/dsk2/tape17/PQDD_0014/MQ34105.pdf.

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41

Nemer, Elias J. "Speech analysis and quality enhancement using higher order cumulants." Thesis, National Library of Canada = Bibliothèque nationale du Canada, 1999. http://www.collectionscanada.ca/obj/s4/f2/dsk1/tape8/PQDD_0020/NQ48333.pdf.

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42

Nemer, Elias J. Carleton University Dissertation Engineering Systems and Computer. "Speech analysis and quality enhancement using higher order cumulants." Ottawa, 1999.

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43

Ankele, Michael Peter [Verfasser]. "Higher-Order Tensors and Differential Topology in Diffusion MRI Modeling and Visualization / Michael Peter Ankele." Bonn : Universitäts- und Landesbibliothek Bonn, 2019. http://d-nb.info/1188731769/34.

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Ankele, Michael [Verfasser]. "Higher-Order Tensors and Differential Topology in Diffusion MRI Modeling and Visualization / Michael Peter Ankele." Bonn : Universitäts- und Landesbibliothek Bonn, 2019. http://d-nb.info/1188731769/34.

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45

Singh, Pranav. "High accuracy computational methods for the semiclassical Schrödinger equation." Thesis, University of Cambridge, 2018. https://www.repository.cam.ac.uk/handle/1810/274913.

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The computation of Schrödinger equations in the semiclassical regime presents several enduring challenges due to the presence of the small semiclassical parameter. Standard approaches for solving these equations commence with spatial discretisation followed by exponentiation of the discretised Hamiltonian via exponential splittings. In this thesis we follow an alternative strategy${-}$we develop a new technique, called the symmetric Zassenhaus splitting procedure, which involves directly splitting the exponential of the undiscretised Hamiltonian. This technique allows us to design methods tha
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46

Dingman, James Steven. "The development and application of generalized higher order filtering techniques to the continuum wave equations /." The Ohio State University, 1986. http://rave.ohiolink.edu/etdc/view?acc_num=osu1487268021749887.

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47

Yano, Masayuki Ph D. Massachusetts Institute of Technology. "An optimization framework for adaptive higher-order discretizations of partial differential equations on anisotropic simplex meshes." Thesis, Massachusetts Institute of Technology, 2012. http://hdl.handle.net/1721.1/76090.

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Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Aeronautics and Astronautics, 2012.<br>Cataloged from PDF version of thesis.<br>Includes bibliographical references (p. 271-281).<br>Improving the autonomy, efficiency, and reliability of partial differential equation (PDE) solvers has become increasingly important as powerful computers enable engineers to address modern computational challenges that require rapid characterization of the input-output relationship of complex PDE governed processes. This thesis presents work toward development of a versatile PDE solver that accurat
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48

Bilyeu, David L. "A HIGHER-ORDER CONSERVATION ELEMENT SOLUTION ELEMENT METHOD FOR SOLVING HYPERBOLIC DIFFERENTIAL EQUATIONS ON UNSTRUCTURED MESHES." The Ohio State University, 2014. http://rave.ohiolink.edu/etdc/view?acc_num=osu1396877409.

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49

Rangaswami, Roopa. "A cost analysis for a higher-order parallel programming model." Thesis, University of Edinburgh, 1996. http://hdl.handle.net/1842/747.

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Programming parallel computers remains a difficult task. An ideal programming environment should enablethe user to concentrate on the problem solving activity at a convenient level of abstraction, while managing the intricate low-level details without sacrificing performance. This thesis investigates a model of parallel programming based on the Bird-Meertens Formalism (BMF). This is a set of higher-order functions, many of which are implicitly parallel. Programs are expressed in terms of functions borrowed from BMF. A parallel implementation is defined for each of these functions for a particu
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鍾偉昌 and Wai-cheong Chung. "Geometrically nonlinear analysis of plates using higher order finite elements." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 1986. http://hub.hku.hk/bib/B31207601.

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