The Reproducing Kernel Hilbert Space Method for Solving System of Linear Weakly Singular Volterra Integral Equations
Journal Title: JOURNAL OF ADVANCES IN MATHEMATICS - Year 2018, Vol 15, Issue 0
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.
Authors and Affiliations
Hameeda Oda Al-Humedi
Intransitive Permutation Groups with Bounded Movement Having Maximum Degree
Let G be a permutation group on a set with no fixed points in and let m be a positive integer. If for each subset of the size is bounded, for , we define the movement of g as the max over...
Combined effects of Hall current and variable Viscosity on Non-Newtonian MHD flow past a stretching vertical plate
This paper investigate the effects of Hall currents on free-convective steady laminar boundary-layer flow, past a semi-infinite vertical plate, for large temperature differences . A uniform magnetic field is applied perp...
On Contra -wgrα-Continuous and Almost Contra-wgrα-Continuous Functions
In this paper a new class of function called contra-wgrα continuous function is introduced and its properties are studied. Further the notion of almost contra wgrα-continuous function is introduced.
Coupled Fixed Point Theorems with CLRg property in Fuzzy Metric Spaces .
In this paper, we prove common coupled fixed point theorems by using E.A. property and CLRg property for coupled mappings without exploiting the notion of continuity, completeness of the whole space or...
Effect of Delta Operator on Umbral Composition in Finite Operator calculus
The main objective of this paper is to propose the matrix representation of umbral composition and investigate the effect of delta operator on umbral composition by using the sequential representation of delta operator i...