Numerical solution of integro-differential equations of high order by wavelet basis, its algorithm and convergence analysis

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:325

Article

Babaaghaie, A.¹  Maleknejad, K.¹ 

[1] Islamic Azad Univ, Karaj Branch, Dept Math, Karaj, Iran

关键词: Fredholm integro-differential equation;    Wavelet Galerkin method;    Wavelets basis;    Convergence analysis;   

DOI  :  10.1016/j.cam.2017.04.035

来源: Elsevier

【 摘 要 】

This paper presents, for the first time, numerical solutions for this particular type of integro-differential equations. According to equations which will be introduced, suitable wavelet Galerkin method is provided using wavelet basis in the space C-alpha (R) boolean AND L-2(R), alpha > 0, that C-alpha (R) is the Holder space of exponent alpha. This approach has two advantages. First, the wavelets basis are arbitrary. It means that any differentiable wavelets basis can be used. Second, the desired orders for this equation are the reasons for involving a wide variety of these types of equations. The Algorithm and convergence analysis of this scheme are described. Numerical examples, plots and tablets of errors confirm the applicability and the validity of the proposed method. (C) 2017 Elsevier B.V. All rights reserved.

【 授权许可】

Free