Investigation approach for a nonlinear singular Fredholm integro-differential equation. (English) Zbl 07801877
Summary: In this paper, we examine the existence and uniqueness of the solution of nonlinear integrodifferential Fredholm equation with a weakly singular kernel. Then, we develop an iterative scheme to approach this solution using the product integration method. Finally, we conclude with a numerical test to show the effectiveness of the proposed method.
MSC:
| 45B05 | Fredholm integral equations |
| 45G05 | Singular nonlinear integral equations |
| 45J99 | Integro-ordinary differential equations |
| 45E99 | Singular integral equations |
| 65R20 | Numerical methods for integral equations |
Keywords:
Fredholm integro-differential equation; singular kernel; fixed point; nonlinear equation; product integration methodReferences:
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