Superconvergent Nyström method for Urysohn integral equations

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• 作者：Chafik Allouch ; Driss Sbibih ; Mohamed Tahrichi
• 关键词：Urysohn equations ; Nyström method ; Gauss points ; Superconvergence
• 刊名：BIT Numerical Mathematics
• 出版年：2017
• 出版时间：March 2017
• 年：2017
• 卷：57
• 期：1
• 页码：3-20
• 全文大小：
• 刊物类别：Mathematics and Statistics
• 刊物主题：Computational Mathematics and Numerical Analysis; Numeric Computing; Mathematics, general;
• 出版者：Springer Netherlands
• ISSN：1572-9125
• 卷排序：57

文摘

Integral equations occur naturally in many fields of mechanics and mathematical physics. In this paper a superconvergent Nyström method has been used for solving one of the most important cases in nonlinear integral equations which is called Urysohn form. Using an interpolatory projection at the set of r Gauss points, it is shown that the proposed method has an order of 3r and one step of iteration improve the convergence order to 4r. The size of the nonlinear system of equations that must be solved to calculate the approximate solution using this method remains the same as the range of the interpolatory projection. Numerical results are given to illustrate the improvement of the order.