An improved reproducing kernel method for Fredholm integro-differential type two-point boundary value problems. (English) Zbl 1499.30314
Summary: In this work, an improved reproducing kernel method to find the numerical solution of Fredholm integro-differential equation type boundary value problems has been developed. Based on the good properties of reproducing kernel function and the conjugate operator, the solution representation is obtained. Meanwhile, we prove that the approximation converges to the exact solution uniformly. After that the convergence estimates are derived.
MSC:
| 30E25 | Boundary value problems in the complex plane |
| 65L03 | Numerical methods for functional-differential equations |
| 47B32 | Linear operators in reproducing-kernel Hilbert spaces (including de Branges, de Branges-Rovnyak, and other structured spaces) |
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