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Dissertations / Theses on the topic 'Integral Solutions'

Author: Grafiati

Published: 3 June 2025

Last updated: 31 July 2025

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1

Cuminato, José Alberto. "Numerical solutions of Cauchy integral equations and applications." Thesis, University of Oxford, 1987. http://ora.ox.ac.uk/objects/uuid:434954bb-bf08-448b-9e02-9948d1287e37.

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This thesis investigates the polynomial collocation method for the numerical solution of Cauchy type integral equations and the use of those equations and the related numerical techniques to solve two practical problem in Acoustics and Aerodynamics. Chapters I and II include the basic background material required for the development of the main body of the thesis. Chapter I discusses a number of practical problems which can be modelled as a singular integral equations. In Chapter II the theory of those equations is given in great detail. In Chapter III the polynomial collocation method for sin

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2

Houghton, Samuel. "Integral-Based Inverse Problem Solutions for DIET Systems." Thesis, University of Canterbury. Mechanical Engineering, 2007. http://hdl.handle.net/10092/1138.

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Magnetic Resonance Elastography (MRE) is an emerging method for non-invasive breast cancer screening. It takes the MRI displacement data output and reconstructs the internal stiffness distribution, where cancerous tissue is approximately five to ten times stiffer than healthy breast tissue. Hence, MRE offers a high contrast solution to this diagnostic problem. Current MRE methods for reconstructing stiffness use forward simulation based optimization methods that are highly non-linear, non-convex and very heavy computationally. This research develops integral-based inverse problem solutions

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3

Houghton, Samuel John. "Integral-based inverse problem solutions for DIET systems." Thesis, University of Canterbury. Mechanical Engineering, 2006. http://hdl.handle.net/10092/6614.

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Magnetic Resonance Elastography (MRE) is an emerging method for non-invasive breast cancer screening. It takes the MRI displacement data output and reconstructs the internal stiffness distribution, where cancerous tissue is approximately five to ten times stiffer than healthy breast tissue. Hence, MRE offers a high contrast solution to this diagnostic problem. Current MRE methods for reconstructing stiffness use forward simulation based optimization methods that are highly non-linear, non-convex and very heavy computationally. This research develops integral-based inverse problem solutions tha

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4

Lee, June-Bok. "Integral solutions in arithmetic progression for elliptic curves." Diss., The University of Arizona, 1991. http://hdl.handle.net/10150/185436.

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Integral solutions to y² = X³ + k, where either the x's or the y's, or both, are in arithmetic progression are studied. When both the x's and the y's are in arithmetic progression, then this situation is completely solved. One set of solutions where the y's formed an arithmetic progression of length 4 have already been constructed. In this dissertation, we construct infinitely many set of solutions where there are 4 x's in arithmetic progression and we also disprove Mohanty's Conjecture[8] by constructing infinitely many set of solutions where there are 4, 5 and 6 y's in arithmetic progression

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5

Hibbs, T. T. "C'('1') continuous representations and advanced singular kernal integrations in the three dimensional boundary integral method." Thesis, Teesside University, 1988. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.384606.

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6

Sipiläinen, Eeva-Maria. "Pathwise view on solutions of stochastic differential equations." Thesis, University of Edinburgh, 1993. http://hdl.handle.net/1842/8202.

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The Ito-Stratonovich theory of stochastic integration and stochastic differential equations has several shortcomings, especially when it comes to existence and consistency with the theory of Lebesque-Stieltjes integration and ordinary differential equations. An attempt is made firstly, to isolate the path property, possessed by almost all Brownian paths, that makes the stochastic theory of integration work. Secondly, to construct a new concept of solutions for differential equations, which would have the required consistency and continuity properties, within a class of deterministic noise func

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7

Sockell, Michael Elliot. "Similarity solutions of stochastic nonlinear parabolic equations." Diss., Virginia Polytechnic Institute and State University, 1987. http://hdl.handle.net/10919/49898.

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A novel statistical technique introduced by Besieris is used to study solutions of the nonlinear stochastic complex parabolic equation in the presence of two profiles. Specifically, the randomly modulated linear potential and the randomly perturbed quadratic focusing medium. In the former, a class of solutions is shown to admit an exact statistical description in terms of the moments of the wave function. In the latter, all even-order moments are computed exactly, whereas the odd-order moments are solved asymptotically. Lastly, it is shown that this statistical technique is isomorphic to mappi

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8

Svensson, Anders. "Path Integral for the Hydrogen Atom : Solutions in two and three dimensions." Thesis, Karlstads universitet, Institutionen för ingenjörsvetenskap och fysik, 2016. http://urn.kb.se/resolve?urn=urn:nbn:se:kau:diva-44425.

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The path integral formulation of quantum mechanics generalizes the action principle of classical mechanics. The Feynman path integral is, roughly speaking, a sum over all possible paths that a particle can take between fixed endpoints, where each path contributes to the sum by a phase factor involving the action for the path. The resulting sum gives the probability amplitude of propagation between the two endpoints, a quantity called the propagator. Solutions of the Feynman path integral formula exist, however, only for a small number of simple systems, and modifications need to be made when d

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9

Tenwick, Michelle Claire. "Error estimates for numerical solutions of one- and two-dimensional integral equations." Thesis, University of Leeds, 2012. http://etheses.whiterose.ac.uk/3405/.

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This thesis is concerned with the improvement of numerical methods, specifically boundaryelement methods (BEMs), for solving Fredholm integral equations in both one- and two dimensions. The improvements are based on novel (computer-algebra-based) error analyses that yield explicit forms of correction terms for a priori incorporation into BEM methods employing piecewise-polynomial interpolation in the numerical approximation. The work is motivated by the aim of reducing errors of BEM methods for low-degree interpolating polynomials, without significantly increasing the computational cost associ

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10

Sagheer, Muhammad. "Mathematical analysis and numerical solutions of an integral equation arising from population dynamics." Thesis, University of Sussex, 2005. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.420495.

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11

Scully, Noelle Catherine. "Semiclassical phase-integral solutions of a Fokker-Planck equation for a ferromagnetic particle." Thesis, Queen's University Belfast, 1993. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.333834.

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12

SHELLEY, MICHAEL JOHN. "THE APPLICATION OF BOUNDARY INTEGRAL TECHNIQUES TO MULTIPLY CONNECTED DOMAINS (VORTEX METHODS, EULER EQUATIONS, FLUID MECHANICS)." Diss., The University of Arizona, 1985. http://hdl.handle.net/10150/188100.

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Very accurate methods, based on boundary integral techniques, are developed for the study of multiple, interacting fluid interfaces in an Eulerian fluid. These methods are applied to the evolution of a thin, periodic layer of constant vorticity embedded in irrotational fluid. Numerical regularity experiments are conducted and suggest that the interfaces of the layer develop a curvature singularity in infinite time. This is to be contrasted with the more singular vorticity distribution of a vortex sheet developing such a singularity in a finite time.

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13

Hao, Han. "Traveling Wave Solutions of Integro-differential Equations of One-dimensional Neuronal Networks." Thèse, Université d'Ottawa / University of Ottawa, 2013. http://hdl.handle.net/10393/24244.

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Traveling wave solutions of integro-differential equations for modeling one-dimensional neuronal networks, are studied. Under moderate continuity assumptions, necessary and sufficient conditions for the existence and uniqueness of monotone increasing (decreasing) traveling wave solutions are established. Some faults in previous studies are corrected.

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14

Kipp, Robert. "Mixed potential integral equation solutions for layered media structures : high frequency interconnects and frequency selective surfaces /." Thesis, Connect to this title online; UW restricted, 1993. http://hdl.handle.net/1773/5974.

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15

in, dani@math tifr res. "On Orbits of SL(2,Z)$_+$ and Values of Binary Quadratic Forms on Positive Integral Pairs." ESI preprints, 2001. ftp://ftp.esi.ac.at/pub/Preprints/esi1050.ps.

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16

Valente, Maria Serra. "Stability of non-trivial solutions of stochastic differential equations driven by the fractional Brownian motion." Master's thesis, Instituto Superior de Economia e Gestão, 2019. http://hdl.handle.net/10400.5/18993.

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Mestrado em Mathematical Finance<br>O objectivo desta dissertação é o de generalizar um resultado sobre a estabilidade exponencial de soluções triviais de equações diferenciais estocásticas com movimento Browniano fraccionário, desenvolvido por Garrido-Atienza et al., para soluções não-triviais. São apresentadas noções de cálculo fraccionário, assim como a definição e principias propriedades do movimento Browniano fraccionário. De seguida, um framework para equações diferenciais estocásticas com movimento Browniano fraccionário é definido juntamente com resultados de existência e unicidade de

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17

MAZZOLA, MARCO. "Properties of solutions to variational problems." Doctoral thesis, Università degli Studi di Milano-Bicocca, 2010. http://hdl.handle.net/10281/18339.

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In the context of the variational problems related to integral functionals, we study some necessary conditions for a solution u without standard growth assumptions and strong differentiability conditions on the Lagrangian L. In particular, we investigate the validity of the Euler-Lagrange equation, in its classical and non-classical form, in the cases of functionals with non-differentiable convex Lagrangian or with super-exponential growth for L. Moreover, we investigate the regularity properties for minimizers, concerning higher integrability of the gradient as well as higher differentiabilit

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18

Ramirez, Gálvez Orlando Arturo, Linares Milagros Cecilia del Carmen Rodríguez, and Elliot Maria del Pilar Zeballos. "Plan de negocios para un centro de belleza integral en el distrito de San Borja." Master's thesis, Universidad Peruana de Ciencias Aplicadas (UPC), 2021. http://hdl.handle.net/10757/654999.

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Existen centros estéticos, cosméticos y de belleza en la ciudad de Lima enfocados en brindar bienestar físico, asimismo, consultorios de nutrición y psicoterapia que preparan un programa para cada paciente. Sin embargo, no se detectan empresas que brinden soluciones integrales: bienestar físico, nutricional y de life coaching en un sólo lugar. El presente plan de negocio propone implementar un centro de belleza integral que partirá de un diagnóstico de un coach. Se ofrecerá una gama de servicios, desde el life coaching, tratamientos estéticos, cosméticos y nutrición, con el objetivo que los

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19

Kokkinos, Filis-Triantaphyllos T. "Three-dimensional layerwise modeling of layered media with boundary integral equations." Diss., This resource online, 1995. http://scholar.lib.vt.edu/theses/available/etd-02132009-170805/.

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20

Martins, Camila Aversa [UNESP]. "Existência de solução de equações integrais não lineares em escalas temporais sobre espaços de Banach." Universidade Estadual Paulista (UNESP), 2013. http://hdl.handle.net/11449/86515.

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Made available in DSpace on 2014-06-11T19:22:18Z (GMT). No. of bitstreams: 0 Previous issue date: 2013-06-27Bitstream added on 2014-06-13T19:48:20Z : No. of bitstreams: 1 martins_ca_me_sjrp.pdf: 297081 bytes, checksum: 4a6f13bdad08f9e72c8df07186762615 (MD5)<br>Neste trabalho estabelecemos condições para a existência e unicidade de solução para equações integrais do tipo Volterra–Stieltjes não linear x(t)+ Z [a,t]T DsK(t,s) f (s,x(s)) = u(t), t E [a,b]T em escalas temporais T, usando a integral de Cauchy–Stieltjes à direita sobre funções regradas a valores em espaços de Banach<br>In this work

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21

Martins, Camila Aversa. "Existência de solução de equações integrais não lineares em escalas temporais sobre espaços de Banach /." São José do Rio Preto, 2013. http://hdl.handle.net/11449/86515.

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Orientador: Luciano Barbanti<br>Coorientador: Geraldo Nunes Silva<br>Banca: German Jesus Lozada Cruz<br>Banca: Márcia Cristina Anderson Braz Federson<br>Resumo: Neste trabalho estabelecemos condições para a existência e unicidade de solução para equações integrais do tipo Volterra-Stieltjes não linear x(t)+ Z [a,t]T DsK(t,s) f (s,x(s)) = u(t), t E [a,b]T em escalas temporais T, usando a integral de Cauchy-Stieltjes à direita sobre funções regradas a valores em espaços de Banach<br>Abstract: In this work we establish conditions for the existence and uniqueness of solution a Volterra- Stieltjes

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22

Jeong, Jaehoon. "Analytical time domain electromagnetic field propagators and closed-form solutions for transmission lines." [College Station, Tex. : Texas A&M University, 2006. http://hdl.handle.net/1969.1/ETD-TAMU-1105.

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23

Zhou, Shuang. "Studies on summability of formal solution to a cauchy problem and on integral functions of Mordell’s type." Thesis, Lille 1, 2010. http://www.theses.fr/2010LIL10058/document.

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Dans cette Thèse, nous considérons dans le plan complexe l’équation de la chaleur avec la condition initiale singulière u(0,z)=1/(1-exp(z)). Ce problème de Cauchy possède une unique solution formelle série entière, laquelle peut être sommée par des procédés de sommation différents. Le but est d’établir des relations existant entre les différentes sommes ainsi étudiées: d’une part la somme de Borel de celle-ci et, de l’autre, deux versions q-analogues de la somme de Borel qui sont obtenuesrespectivement avec le noyau de la chaleur et la fonction thêta de Jacobi. Notre analyse sur le phénomène d

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24

Wu, Yue. "Pathwise anticipating random periodic solutions of SDEs and SPDEs with linear multiplicative noise." Thesis, Loughborough University, 2014. https://dspace.lboro.ac.uk/2134/15991.

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In this thesis, we study the existence of pathwise random periodic solutions to both the semilinear stochastic differential equations with linear multiplicative noise and the semilinear stochastic partial differential equations with linear multiplicative noise in a Hilbert space. We identify them as the solutions of coupled forward-backward infinite horizon stochastic integral equations in general cases, and then perform the argument of the relative compactness of Wiener-Sobolev spaces in C([0, T],L2Ω,Rd)) or C([0, T],L2(Ω x O)) and Schauder's fixed point theorem to show the existence of a sol

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25

Keblikas, Vaidas. "Time periodic problems for Navier-Stokes equations in domains with cylindrical outlets to infinity." Doctoral thesis, Lithuanian Academic Libraries Network (LABT), 2008. http://vddb.library.lt/obj/LT-eLABa-0001:E.02~2008~D_20081119_134254-90799.

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The research area of current PhD thesis is the analysis of time periodic Navier-Stokes equations in domains with cylindrical outlets to infinity. The objects of investigation is so called non-statonary Poiseuille solution in the straight cylinder and Navier-Stokes equations in system of cylinders.<br>Disertacijoje nagrinėjami Navjė-Stokso lygčių periodiniai laiko atžvilgiu uždaviniai srityse su cilindriniais išėjimais į begalybę. Pagrindiniai tyrimo objektai yra taip vadinami Puazelio sprendiniai tiesiame cilindre ir Stokso, bei Navjė-Stokso lygčių sistemos cilindrų sistemoje.

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26

Tani, Fatima. "Periodic control of multi-specific bioreactors in order to optimize their performances." Thesis, Montpellier, 2019. http://www.theses.fr/2019MONTS058.

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Les contributions de ce travail sont présentées en deux parties. Nous considérons d’abord un problème de contrôle optimal périodique régi par un système dynamique scalaire, linéaire par rapport à la variable de contrôle satisfaisant une contrainte intégrale. Nous présentons des conditions suffisantes permettant de déduire l’existence d’un sur-rendement qui consiste à améliorer le critère à l’équilibre associé un contrôle constant ū en considérant un contrôle périodique u avec une valeur moyenne égale à ū. Nous utilisons le Principe de Maximum de Pontryagin pour conclure la synthèse optimale pé

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27

Harbrecht, Helmut, and Reinhold Schneider. "Wavelet based fast solution of boundary integral equations." Universitätsbibliothek Chemnitz, 2006. http://nbn-resolving.de/urn:nbn:de:swb:ch1-200600649.

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This paper presents a wavelet Galerkin scheme for the fast solution of boundary integral equations. Wavelet Galerkin schemes employ appropriate wavelet bases for the discretization of boundary integral operators which yields quasi-sparse system matrices. These matrices can be compressed such that the complexity for solving a boundary integral equation scales linearly with the number of unknowns without compromising the accuracy of the underlying Galerkin scheme. Based on the wavelet Galerkin scheme we present also an adaptive algorithm. By numerical experiments we provide results which demonst

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28

Mendes, Wendy R. "The numerical solution of Wiener-Hopf integral equations." Thesis, University of Bath, 1988. https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.383599.

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29

Sooman, Craig. "Soliton solutions of noncommutative integrable systems." Thesis, University of Glasgow, 2010. http://theses.gla.ac.uk/1449/.

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This thesis is concerned with solutions of noncommutative integrable systems where the noncommutativity arises through the dependent variables in either the hierarchy or Lax pair generating the equation. Both Chapters 1 and 2 are entirely made up of background material and contain no new material. Furthermore, these chapters are concerned with commutative equations. Chapter 1 outlines some of the basic concepts of integrable systems including historical attempts at finding solutions of the KdV equation, the Lax method and Hirota's direct method for finding multi-soliton solutions of an integra

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30

Macfarlane, Susan R. "Quasideterminant solutions of noncommutative integrable systems." Thesis, University of Glasgow, 2010. http://theses.gla.ac.uk/1887/.

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Quasideterminants are a relatively new addition to the field of integrable systems. Their simple structure disguises a wealth of interesting and useful properties, enabling solutions of noncommutative integrable equations to be expressed in a straightforward and aesthetically pleasing manner. This thesis investigates the derivation and quasideterminant solutions of two noncommutative integrable equations - the Davey-Stewartson (DS) and Sasa-Satsuma nonlinear Schrodinger (SSNLS) equations. Chapter 1 provides a brief overview of the various concepts to which we will refer during the course of th

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31

Nicoll, Wilfred James. "Global oscillatory integrals for solutions of hyperbolic systems." Thesis, University of Sussex, 1999. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.266443.

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32

Berger, Bryan William. "Protein-surfactant solution thermodynamics applications to integral membrane proteins /." Access to citation, abstract and download form provided by ProQuest Information and Learning Company; downloadable PDF file 15.42 Mb., 304 p, 2006. http://gateway.proquest.com/openurl?url_ver=Z39.88-2004&res_dat=xri:pqdiss&rft_val_fmt=info:ofi/fmt:kev:mtx:dissertation&rft_dat=xri:pqdiss:3200533.

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33

Harbrecht, Helmut, and Reinhold Schneider. "Wavelets for the fast solution of boundary integral equations." Universitätsbibliothek Chemnitz, 2006. http://nbn-resolving.de/urn:nbn:de:swb:ch1-200600540.

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This paper presents a wavelet Galerkin scheme for the fast solution of boundary integral equations. Wavelet Galerkin schemes employ appropriate wavelet bases for the discretization of boundary integral operators. This yields quasi-sparse system matrices which can be compressed to O(N_J) relevant matrix entries without compromising the accuracy of the underlying Galerkin scheme. Herein, O(N_J) denotes the number of unknowns. The assembly of the compressed system matrix can be performed in O(N_J) operations. Therefore, we arrive at an algorithm which solves boundary integral equations within opt

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34

Mohamed, Nurul Akmal. "Numerical solution and spectrum of boundary-domain integral equations." Thesis, Brunel University, 2013. http://bura.brunel.ac.uk/handle/2438/7592.

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A numerical implementation of the direct Boundary-Domain Integral Equation (BDIE)/ Boundary-Domain Integro-Differential Equations (BDIDEs) and Localized Boundary-Domain Integral Equation (LBDIE)/Localized Boundary-Domain Integro-Differential Equations (LBDIDEs) related to the Neumann and Dirichlet boundary value problem for a scalar elliptic PDE with variable coefficient is discussed in this thesis. The BDIE and LBDIE related to Neumann problem are reduced to a uniquely solvable one by adding an appropriate perturbation operator. The mesh-based discretisation of the BDIE/BDIDEs and LBDIE/LBDID

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35

Minezawa, Noriyuki. "Integral equation studies on solute electronic structures in solution." 京都大学 (Kyoto University), 2008. http://hdl.handle.net/2433/136920.

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36

Poole, Mark W. "Numerical solution of an electropaint problem." Thesis, Cranfield University, 1996. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.309789.

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MANESCHY, JOSE E. "Integral-J para carregamentos ciclicos." reponame:Repositório Institucional do IPEN, 1998. http://repositorio.ipen.br:8080/xmlui/handle/123456789/10703.

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Saeed, Usman. "Adaptive numerical techniques for the solution of electromagnetic integral equations." Diss., Georgia Institute of Technology, 2011. http://hdl.handle.net/1853/41173.

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Various error estimation and adaptive refinement techniques for the solution of electromagnetic integral equations were developed. Residual based error estimators and h-refinement implementations were done for the Method of Moments (MoM) solution of electromagnetic integral equations for a number of different problems. Due to high computational cost associated with the MoM, a cheaper solution technique known as the Locally-Corrected Nyström (LCN) method was explored. Several explicit and implicit techniques for error estimation in the LCN solution of electromagnetic integral equations were pro

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39

Yu, Jing. "Iterative Solution of Boundary Integral Equations for Shallow Water Waves." The Ohio State University, 2015. http://rave.ohiolink.edu/etdc/view?acc_num=osu1415056847.

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Santos, Joao Rafael Lucio dos. "Tópicos em defeitos deformados e o movimento Browniano." Universidade Federal da Paraíba, 2013. http://tede.biblioteca.ufpb.br:8080/handle/tede/5748.

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Made available in DSpace on 2015-05-14T12:14:12Z (GMT). No. of bitstreams: 1 arquivototal.pdf: 3660633 bytes, checksum: 7309d28729d29dd071bc87f7c5609ebc (MD5) Previous issue date: 2013-11-20<br>Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES<br>The non-linear science is a central topic covering several investigation areas, such as biology, chemistry, mathematics and physics. In the first part of this thesis, we studied the non-linearity in the scope of classical field theory. The discussions are based on static solutions in (1, 1) space-time dimensions, and they are

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41

Ayyildiz, Kasim. "Surface integral solution of chiral loaded waveguides of arbitrary cross section." Related electronic resource: Current Research at SU : database of SU dissertations, recent titles available full text, 2006. http://proquest.umi.com/login?COPT=REJTPTU0NWQmSU5UPTAmVkVSPTI=&clientId=3739.

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42

Phillips, Joel R. (Joel Reuben). "Rapid solution of potential integral equations in complicated 3-dimensional geometries." Thesis, Massachusetts Institute of Technology, 1997. http://hdl.handle.net/1721.1/43400.

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Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 1997.<br>Includes bibliographical references (p. 133-137).<br>by Joel Reuben Phillips.<br>Ph.D.

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43

Harris, Paul John. "The numerical solution of the dynamic fluid-structure interaction problem." Thesis, University of Plymouth, 1989. http://hdl.handle.net/10026.1/2055.

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In this thesis we consider the problem of the dynamic fluid-structure interaction between a finite elastic structure and the acoustic field in an unbounded fluid-filled exterior domain. We formulate the exterior acoustic problem as an integral equation over the structure surface. However, the classical boundary integral equation formulations of this problem do not have unique solutions at certain characteristic frequencies (which depend on the surface) and it is necessary to employ modified boundary integral equation formulations which are valid for all frequencies. The modified integral equat

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44

Kou, Xin. "Rogue Wave Solutions to Integrable System by Darboux Transformation." ScholarWorks @ UVM, 2014. http://scholarworks.uvm.edu/graddis/306.

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The Darboux transformation is one of the main techniques for finding solutions of integrable equations. The Darboux transformation is not only powerful in the construction of muilti-soliton solutions, recently, it is found that the Darboux transformation, after some modification, is also effective in generating the rogue wave solutions. In this thesis, we derive the rogue wave solutions for the Davey-Stewartson-II (DS-II) equation in terms of Darboux transformation. By taking the spectral function as the product of plane wave and rational function, we get the fundamental rogue wave solution an

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45

Galstyan, Anahit. "Existence and Number of Global Solutions to Model Nonlinear Partial Differential Equations." University of Cincinnati / OhioLINK, 2005. http://rave.ohiolink.edu/etdc/view?acc_num=ucin1115841126.

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Gregory, James Philip. "A q-discrete Analogue of the Third Painlevé Equation and its Linear Problem." Thesis, The University of Sydney, 2016. http://hdl.handle.net/2123/15470.

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In this thesis we investigate the rational and Riccati type special solutions for particular parameter values of a q-discrete analogue of the third Painlevé equation, with rational surface A(1) 5 and affine Weyl group (A2 + A1)(1). The general solutions of this equation are highly transcendental in nature. We work closely with an associated system of discrete linear equations, which we refer to as ‘the linear problem.’We demonstrate that the linear problem can be solved both in terms of q-Gamma functions and series expansions for different parameter values of our discrete Painlevé equation. By

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Abdulla, Dalya. "An integral formulation for the solution of a nonlinear wave-propagation problem." Thesis, National Library of Canada = Bibliothèque nationale du Canada, 2000. http://www.collectionscanada.ca/obj/s4/f2/dsk2/ftp03/MQ57211.pdf.

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Cheng, Jin. "Formulation and Solution of Electromagnetic Integral Equations Using Constraint-Based Helmholtz Decompositions." UKnowledge, 2012. http://uknowledge.uky.edu/ece_etds/11.

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This dissertation develops surface integral equations using constraint-based Helmholtz decompositions for electromagnetic modeling. This new approach is applied to the electric field integral equation (EFIE), and it incorporates a Helmholtz decomposition (HD) of the current. For this reason, the new formulation is referred to as the EFIE-hd. The HD of the current is accomplished herein via appropriate surface integral constraints, and leads to a stable linear system. This strategy provides accurate solutions for the electric and magnetic fields at both high and low frequencies, it allows for t

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Tinniswood, Adam D. "Solution of time domain integral equations on distributed memory parallel processing systems." Thesis, University of York, 1995. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.362022.

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Yoshida, Norio. "Theoretical study on solute electronic strucures in solution; Integral equation ap-proach." 京都大学 (Kyoto University), 2003. http://hdl.handle.net/2433/149107.

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