Analytical and computational methods for a class of nonlinear singular integral equations

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• 作者：Sonia Seyed Allaei^a ; ^b ; ^{soniase@gmail.com} ; Teresa Diogo^b ; ^{tdiogo@math.ist.utl.pt} ; Magda Rebelo^c ; ^{msjr@fct.unl.pt}
• 关键词：Nonlinear Volterra integral equation ; Weakly singular kernel ; Hammerstein equations ; Iterative solution ; Product integration method
• 刊名：Applied Numerical Mathematics
• 出版年：2017
• 出版时间：April 2017
• 年：2017
• 卷：114
• 期：Complete
• 页码：2-17
• 全文大小：415 K
• 卷排序：114

文摘

We consider a class of nonlinear singular Hammerstein Volterra integral equations. In general, these equations will have kernels containing both an end point and an Abel-type singularity, with exact solutions being typically nonsmooth. Under certain conditions, a uniformly convergent iterative solution is obtained on a small interval near the origin. In this work, two product integration methods are proposed and analyzed where the integral over a small initial interval is calculated analytically, allowing the optimal convergence rates to be achieved. This is illustrated by some numerical examples.