# A Galerkin-like approach to solve high-order integrodifferential equations with weakly singular kernel

## Keywords:

Galerkin method, inner product, integro-differential equations, residual error correction, weakly singular kernel.## Abstract

In this study, a Galerkin-like approach is applied to numerically solve high-orderintegro-differential equations having weakly singular kernel. The method includestaking inner product of a set of monomials with a vector obtained from the equationin question. The resulting linear system is then solved, yielding a polynomial as theapproximate solution. Additionally, the technique of residual correction, which aimsto increase the accuracy of the approximate solution, is discussed briefly. Lastly, themethod and the residual correction technique are illustrated with several examples.The results are also compared with numerous existing methods from the literature.## References

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