Numerical Analysis of Alternating Direction Implicit Orthogonal Spline Collocation Scheme for the Hyperbolic Integrodifferential Equation with a Weakly Singular Kernel

Abstract

This paper studies an alternating direction implicit orthogonal spline collocation (ADIOSC) technique for calculating the numerical solution of the hyperbolic integrodifferential problem with a weakly singular kernel in the two-dimensional domain. The integral term is approximated with the help of the second-order fractional quadrature formula introduced by Lubich. The stability and convergence analysis of the proposed strategy are proven in L2-norm. Numerical results highlight the high accuracy and efficiency of the proposed strategy and clarify the theoretical prediction.