Quasi wavelet based numerical method for a class of partial integro-differential equation

被引：21

作者：

Long, Wenting ^{[2
]}

Xu, Da ^{[1
]}

Zeng, Xueying ^{[3
]}

机构：

[1] Hunan Normal Univ, Coll Math & Comp Sci, Changsha 410081, Hunan, Peoples R China

[2] Sun Yat Sen Univ, Sch Math & Computat Sci, Guangzhou 510275, Guangdong, Peoples R China

[3] Ocean Univ China, Sch Math Sci, Qingdao 266100, Peoples R China

来源：

APPLIED MATHEMATICS AND COMPUTATION | 2012年 / 218卷 / 24期

关键词：

Partial integro-differential equation; Quasi-wavelets; Forward Euler method; Regularization; Numerical method; DISCRETE SINGULAR CONVOLUTION; EVOLUTION EQUATION; MEMORY TERM; DISCRETIZATION; APPROXIMATIONS;

D O I：

10.1016/j.amc.2012.04.090

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper we study the numerical solution of initial-boundary problem for a class of partial integro-differential equations. The quasi wavelet method is proposed to handle the spatial derivatives while the forward Euler method is used to discretize the temporal derivatives. Detailed discrete schemes are given and some numerical experiments are included to demonstrate the effectiveness of the discrete technique. The comparisons of the present numerical results with the exact analytical solutions show that the quasi wavelet based numerical method has distinctive local property and can achieve accurate results. (C) 2012 Elsevier Inc. All rights reserved.

引用

页码：11842 / 11850

页数：9

共 27 条

[1] Orthogonal spline collocation methods for partial differential equations [J].

Bialecki, B ;

Fairweather, G .

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2001, 128 (1-2) :55-82

[2] FINITE-ELEMENT APPROXIMATION OF A PARABOLIC INTEGRODIFFERENTIAL EQUATION WITH A WEAKLY SINGULAR KERNEL [J].

CHEN, C ;

THOMEE, V ;

WAHLBIN, LB .

MATHEMATICS OF COMPUTATION, 1992, 58 (198) :587-602

[3] NONSMOOTH INITIAL DATA ERROR-ESTIMATES WITH THE WEIGHT NORMS FOR THE LINEAR FINITE-ELEMENT METHOD OF PARABOLIC PARTIAL-DIFFERENTIAL EQUATIONS [J].

DA, X .

APPLIED MATHEMATICS AND COMPUTATION, 1993, 54 (01) :1-24

[4] SPLINE COLLOCATION METHODS FOR A CLASS OF HYPERBOLIC PARTIAL INTEGRODIFFERENTIAL EQUATIONS [J].

FAIRWEATHER, G .

SIAM JOURNAL ON NUMERICAL ANALYSIS, 1994, 31 (02) :444-460

[5]

HUANG YQ, 1994, J COMPUT MATH, V12, P259

[6] Numerical solution of parabolic integro-differential equations by the discontinuous Galerkin method [J].

Larsson, S ;

Thomee, V ;

Wahlbin, LB .

MATHEMATICS OF COMPUTATION, 1998, 67 (221) :45-71

[7]

Lin T., 2001, SIAM J NUMER ANAL, P937

[8] Finite difference/spectral approximations for the time-fractional diffusion equation [J].

Lin, Yumin ;

Xu, Chuanju .

JOURNAL OF COMPUTATIONAL PHYSICS, 2007, 225 (02) :1533-1552

[9] DISCRETIZED FRACTIONAL CALCULUS [J].

LUBICH, C .

SIAM JOURNAL ON MATHEMATICAL ANALYSIS, 1986, 17 (03) :704-719

[10] MULTIRESOLUTION APPROXIMATIONS AND WAVELET ORTHONORMAL BASES OF L2(R) [J].

MALLAT, SG .

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 1989, 315 (01) :69-87

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