The Reproducing Kernel Hilbert Space Method for Solving System          of Linear Weakly Singular Volterra Integral Equations

Hameeda Oda Al-Humedi

doi:10.24297/jam.v15i0.7869

Authors

Hameeda Oda Al-Humedi university of Basrah, College of Education for Pure Sciences, Mathematics department

DOI:

https://doi.org/10.24297/jam.v15i0.7869

Keywords:

Linear system, weakly singular kernel, Volterra integral equations, Taylor's expansion, reproducing kernel Hilbert space

Abstract

The exact solutions of a system of linear weakly singular Volterra integral equations (VIE) have been a difficult to find. The aim of this paper is to apply reproducing kernel Hilbert space (RKHS) method to find the approximate solutions to this type of systems. At first, we used Taylor's expansion to omit the singularity. From an expansion the given system of linear weakly singular VIE is transform into a system of linear ordinary differential equations (LODEs). The approximate solutions are represent in the form of series in the reproducing kernel space . By comparing with the exact solutions of two examples, we saw that RKHS is a powerful, easy to apply and full efficiency in scientific applications to build a solution without linearization and turbulence or discretization.

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