An improved method based on Haar wavelets for numerical solution of nonlinear integral and integro-differential equations of first and higher orders

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:260

Article

Siraj-ul-Islam¹  Aziz, Imran^1,2  Al-Fhaid, A. S.³ 

[1] Univ Engn & Technol, Dept Basic Sci, Peshawar, Pakistan

[2] Univ Peshawar, Dept Math, Peshawar, Pakistan

[3] King Abdulaziz Univ, Dept Math, Jeddah 21413, Saudi Arabia

关键词: Haar wavelet;    Fredholm integral equations;    Volterra integral equations;    First-order integro-differential equations;    Second-order integro-differential equations;    Fourth-order integro-differential equations;   

DOI  :  10.1016/j.cam.2013.10.024

来源: Elsevier

【 摘 要 】

In this paper, a novel technique is being formulated for the numerical solution of integral equations (lEs) as well as integro-differential equations (IDEs) of first and higher orders. The present approach is an improved form of the Haar wavelet methods (Aziz and Siraj-ul-Islam, 2013, Siraj-ul-Islam et al., 2013). The proposed modifications resulted in computational efficiency and simple applicability of the earlier methods (Aziz and Siraj-ul-Islam, 2013, Siraj-ul-Islam et al., 2013). In addition to this, the new approach is being extended from IDEs of first order to IDEs of higher orders with initial- and boundary-conditions. Unlike the methods (Aziz and Siraj-ul-Islam, 2013, Siraj-ul-Islam et al., 2013) (where the kernel function is being approximated by two-dimensional Haar wavelet), the kernel function in the present case is being approximated by one-dimensional Haar wavelet. The modified approach is easily extendable to higher order IDEs. Numerical examples are being included to show the accuracy and efficiency of the new method. (C) 2013 Elsevier B.V. All rights reserved.

【 授权许可】

Free