Dissertation > Excellent graduate degree dissertation topics show

Several types of Volterra Integral Equations spectral collocation solution and convergence analysis

Author: ChenShaoJun
Tutor: WangQiSheng
School: Wuyi University
Course: Applied Mathematics
Keywords: Volterra integral equation Fredholm-Volterra integral equation Legendre spectral collocation method Chebyshev spectral collocation method Convergence analysis
CLC: O241.83
Type: Master's thesis
Year: 2011
Downloads: 55
Quote: 0
Read: Download Dissertation

Abstract


In this paper, the spectral collocation methods are systematically studied for two-dimensional Volterra integral equations with smooth kernel and Fredholm-Volterra type integral equations.Firstly, the Legendre spectral collocation method and Chebyshev spectral collocation method are proposed to solve the two-dimensional Volterra integral equation. Secondly, we will provide a rigorous convergence analysis which theoretically justifies the spectral rate of the convergence of the proposed method. Finally, the Legendre spectral collocation method is introduced to solve the Fredholm-Volterra integral equation, and the convergence analysis results are given.This paper is organized as follows:In chapterⅠ, the research background of the spectral methods and Volterra integral equa-tion are introduced, and some preliminary knowledge are given.In chapterⅡ, the methods of the numerical solution for the one-dimensional Volterra integral equations are summarized and the main results of this paper are introduced.In chapterⅢ, the Legendre and Chebyshev spectral collocation methods are proposed re-spectively to solve the two-dimensional Volterra integral equations and the convergence analysis results are obtained.In chapterⅣ, the Legendre spectral collocation method is introduced to solve the Fredholm-Volterra integral equation and the convergence analysis result is given.

Related Dissertations

  1. Quasi-Monte Carlo Method for the Structured Stochastic Variational Inequalities,O22
  2. Two-dimensional Fredholm Integral Equations and Convergence Analysis Configuration Solution,O241.83
  3. Augmented Lagrange Algorithms and Applications in Optimization of Wireless Optical Communication System,TN929.1
  4. Terminal Perturbation Methods for Backward Stochastic Volterra Integral Equations,O211.63
  5. A Characteristic Finite Element Scheme for Convention-Dominated Problems,O241.82
  6. Some Studies on Numerical Methods for the Complementarity Problems,O224
  7. Study on Solutions of Two Fuzzy Equations,O159
  8. Business Letters convergence analysis,H319.3
  9. Research on Partial Updating RLS Algorithm,TN911.72
  10. Numerical Realization of an Inverse Problem for 1-Dimensional Wave Equation,O241.6
  11. A Class of Finite Volume Method for Diffusion Equations,O241.82
  12. The Finite Element Method for Solving the Burgers’ Equation Based on the Hope-Cole Transformation,O241.82
  13. Cubic Superconvergent Finite Volume Element Method for One-dimensional Elliptic and Parabolic Equations,O241.82
  14. The Sample Average Approximation Method for the Stochastic Variational Inequality Problem,O212.2
  15. Galerkin Methods for Two Dimensional Shallow Water Equations,O241.82
  16. Research on the Algorithm of Convection-dominated Diffusion of Two Dimensions Based on Characteristic Theory,O241.82
  17. Convergence analysis of the preconditioned Gauss-Seidel iteration method,O241.6
  18. New Numerical Methods Research for Several Option Pricing Modeling,O241.82
  19. Shaanxi Province regional economic disparities and convergence of growth,F127
  20. Research and Application of Intelligence Algorithms in Fuzzy Logic and Fuzzy System,TP18
  21. Two-grid Methods for Expanded Mixed Finite Element Approximations of Nonlinear Parabolic Equations,O241.82

CLC: > Mathematical sciences and chemical > Mathematics > Computational Mathematics > Numerical Analysis > The numerical solution of differential equations, integral equations > Numerical Solution of Integral Equation
© 2012 www.DissertationTopic.Net  Mobile