Pseudocomposition: A technique to design predictor-corrector methods for systems of nonlinear equations

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• 作者：Alicia Cordero ; Juan R. Torregrosa ; Mar¨ªa P. Vassileva
• 关键词：Nonlinear systems ; Iterative methods ; Jacobian matrix ; Convergence order ; Efficiency index
• 刊名：Applied Mathematics and Computation
• 出版年：2012
• 出版时间：1 August, 2012
• 年：2012
• 卷：218
• 期：23
• 页码：11496-11504
• 全文大小：234 K

文摘

A new technique for designing iterative methods for solving nonlinear systems is presented. This procedure, called pseudocomposition, uses a known method as a predictor and the Gaussian quadrature as a corrector. The order of convergence of the resulting scheme depends, among other factors, on the order of the last two steps of the predictor. We also introduce a new iterative algorithm of order six, and apply the mentioned technique to generate a new method of order ten. Finally, some numerical test are shown.