A new approach to the numerical solution of weakly singular Volterra integral equations

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:163

Article

Baratella, P ; Orsi, AP

关键词: product integration;    weakly singular Volterra integral equation;   

DOI  :  10.1016/j.cam.2003.08.047

来源: Elsevier

【 摘 要 】

We consider linear weakly singular Volterra integral equations of the second kind, with kernels of the form k(x, v) = \x - v\(-alpha) K(x, v), 0 < alpha < 1, or k(x, v) = log\x - v\K(x, v), K(x, v) being a smooth function. The solutions of such equations may exhibit a singular behaviour in the neighbourhood of the initial point of the interval of integration. By a transformation of the unknown function we obtain an equation which is still weakly singular, but whose solution is as smooth as we like. This resulting equation is then solved by standard product integration methods. (C) 2003 Elsevier B.V. All rights reserved.

【 授权许可】

Free