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

Document Type : Research Article

Author

• S. Amiri

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

10.22067/ijnao.2023.80420.1211

Abstract

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.

Keywords

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

20.1001.1.24236977.2023.13.3.5.0

Main Subjects

• Numerical methods for integral equations and its applications

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