Numerical Assessment of Symmetric and Non-Symmetric Kernel Functions on Second Order Non-Homogenous Volterra Integro-Differential Equations

Abstract

In this paper, we present numerical assessment of symmetric and non-symmetric kernel functions on non-homogenous Volterra integro-differential equations. Simple MAPLE 18 software commands codes procedures are employ based on newly introduced techniques: exponentially fitted collocation approximation method and Adomian decomposition method for the numerical solutions of the non-homogenous Volterra integro-differential equations. The procedures are sought to obtain convergent point of the problems. Considering the property of symmetric and non-symmetric kernel ( Kt,s=Ks,t and Kt,s≠Ks,t ), the computational lengths are considered to archive the best numerical solutions for the four examples considered. The reliability and efficiency of the proposed techniques are demonstrated using some examples available in literature.

Keywords

• Symmetric and non-symmetric kernel functions
• exponentially fitted collocation approximate method
• non-homogenous Volterra integro-differential equations exponentially fitted collocation approximate method
• Adomian decomposition method

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