Spectral methods for weakly singular Volterra integral equations with smooth solutions
Yanping Chen,Tao Tang +1 more
Reads0
Chats0
TLDR
A rigorous error analysis is provided for the proposed spectral Jacobi-collocation approximation for the linear Volterra integral equations (VIEs) of the second kind with weakly singular kernels, which shows that the numerical errors decay exponentially in the infinity norm and weighted Sobolev space norms.About:
This article is published in Journal of Computational and Applied Mathematics.The article was published on 2009-12-01 and is currently open access. It has received 138 citations till now. The article focuses on the topics: Volterra integral equation & Sobolev space.read more
Citations
More filters
Journal ArticleDOI
Spectral collocation method for linear fractional integro-differential equations
Xiaohua Ma,Chengming Huang +1 more
TL;DR: In this paper, a spectral Jacobi-collocation method for numerical solution of general linear fractional integro-differential equations is proposed and some numerical results are given to demonstrate the effectiveness of the proposed method.
Journal ArticleDOI
Convergence Analysis of Spectral Galerkin Methods for Volterra Type Integral Equations
Ziqing Xie,Xianjuan Li,Tao Tang +2 more
TL;DR: This work is to provide spectral and pseudo-spectral Jacobi-Galerkin approaches for the second kind Volterra integral equation and a rigorous error analysis in both the infinity and weighted norms is given.
Journal ArticleDOI
Convergence analysis of jacobi spectral collocation methods for abel-volterra integral equations of second kind
Xianjuan Li,Tao Tang +1 more
TL;DR: In this article, a spectral Jacobi-collocation approximation for Volterra integral equations with singular kernel ϕ(t, s) = (t − s)−µ is presented.
Journal ArticleDOI
Convergence Analysis of the Spectral Methods for Weakly Singular Volterra Integro-Differential Equations with Smooth Solutions
Yunxia Wei,Yanping Chen +1 more
TL;DR: In this paper, the authors consider the case when the underlying solutions of weakly singular Volterra integro-differential equations are sufficiently smooth and provide a rigorous error analysis for the spectral methods, which shows that both the error of approximate solutions and the errors of approximate derivatives of the solutions decay exponentially in L ¥ -norm and weighted L 2 -norm.
References
More filters
Book
Geometric Theory of Semilinear Parabolic Equations
TL;DR: The neighborhood of an invariant manifold near an equilibrium point is a neighborhood of nonlinear parabolic equations in physical, biological and engineering problems as mentioned in this paper, where the neighborhood of a periodic solution is defined by the invariance of the manifold.
Book
Inverse Acoustic and Electromagnetic Scattering Theory
David Colton,Rainer Kress +1 more
TL;DR: Inverse Medium Problem (IMP) as discussed by the authors is a generalization of the Helmholtz Equation for direct acoustical obstacle scattering in an Inhomogeneous Medium (IMM).
Book
Spectral Methods: Fundamentals in Single Domains
TL;DR: In this article, the authors have incorporated into this new edition the many improvements in the algorithms and the theory of spectral methods that have been made since then, and the discussion of direct and iterative solution methods is also greatly expanded.
MonographDOI
Collocation Methods for Volterra Integral and Related Functional Differential Equations
TL;DR: Collocation based on piecewise polynomial approximation as discussed by the authors is a powerful class of methods for the numerical solution of initial-value problems for functional differential and integral equations arising in a wide spectrum of applications, including biological and physical phenomena.
Related Papers (5)
Convergence analysis of the Jacobi spectral-collocation methods for Volterra integral equations with a weakly singular kernel
Yanping Chen,Tao Tang +1 more