Effective numerical methods for nonlinear singular two-point boundary value Fredholm integro-differential equations

Iranian Journal of Numerical Analysis and Optimization

مقاله 5، دوره 13، شماره 3 - شماره پیاپی 26، آذر 2023، صفحه 444-459   

نوع مقاله: Research Article

شناسه دیجیتال (DOI): 10.22067/ijnao.2023.80420.1211

نویسنده

S. Amiri^*

Department of Basic Sciences, Shahid Sattari Aeronautical University of Science and Technology, P.O. Box: 13846-63113, Tehran, Iran.

چکیده

We deal with some effective numerical methods for solving a class of nonlinear singular two-point boundary value Fredholm integro-differential equations. Using an appropriate interpolation and a q-order quadrature rule of integration, the original problem will be approximated by the non-linear finite difference equations and so reduced to a nonlinear algebraic system that can be simply implemented. The convergence properties of the proposed method are discussed, and it is proved that its convergence order will be of O(hmin{ 72 ,q− 12 }). Ample numerical results are addressed to con-
firm the expected convergence order as well as the accuracy and efficiency of the proposed method.

کلیدواژه‌ها

Nonlinear Fredholm integro-differential equations؛ Singular two-point boundary value؛ Numerical method

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