On the numerical solution of weakly singular integral equations of the first kind using a regularized projection method. (English) Zbl 07889424
Summary: This study investigates a numerical method based on the Jacobi-Gauss quadrature for solving Fredholm integral equations of the first kind with a weakly singular kernel by combining the Tikhonov regularization and projection methods. This numerical method reduces the solution of the weakly singular integral equations of the first kind to the solution of a linear system of algebraic equations. The theoretical analysis of the proposed technique is provided. Finally, several tests are presented to show the validity and efficiency of this approach.
MSC:
| 45B05 | Fredholm integral equations |
| 65J20 | Numerical solutions of ill-posed problems in abstract spaces; regularization |
| 65M30 | Numerical methods for ill-posed problems for initial value and initial-boundary value problems involving PDEs |
Keywords:
ill-posed problems; Tikhonov regularization; Legendre polynomials; Gauss-Jacobi quadrature; weakly singular integral equationsReferences:
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