Meshless procedure for highly oscillatory kernel based one-dimensional Volterra integral equations

Abstract

A meshless procedure with a multi-quadric radial basis function is proposed for the numerical solution of oscillatory Volterra integral equations. Integral operator of the Volterra integral equation is transformed into a differential operator by Liven’s formulation. Consequently, the numerical solution of the differential equation is obtained by a meshless procedure on global and local support domains. Theoretical error bound is derived in the inverse power of the frequency parameter. The proposed technique is also applied to the perturbed form of the Volterra integral equation of the second kind. Perturbation technique is used to overcome challenges in the numerical solution of the Volterra integral equations. Accuracy and efficiency of the proposed procedure are validated through some numerical benchmark problems.