Solving Partial Integro-Differential Equations with Weakly Singular Kernel

Abstract

Equations with a combination of integrals and derivatives are known as integro-differential equations. They are a combination of science and engineering. Many models are implemented with the help of integro-differential equations. Various techniques are available to solve integro-differential equations. In the present study, the Radial Basis Function and Adomain Decomposition Method-based numerical algorithms are used to solve a linear partial integro-differential equation with weakly singular kernel, which arises from viscoelasticity. In the discretization process, singular integrals were compared with the product trapezoidal method. Implementation of various radial basis functions was carried out. The proposed system was found to be useful and to provide reproducible results.