Novel numerical method based on cubic B-splines for a class of nonlinear generalized telegraph equations in irregular domains

Abstract

In this work, a cubic B-spline method based on finite difference and meshless approaches for solving 2D generalized telegraph equations in irregular single and multi-connected domains is presented. The three-layer Crank-Nicolson time-stepping scheme is applied for temporal derivatives and systems of second order elliptic partial differential equations (EPDEs) of general type with mixed derivatives and variable coefficients are obtained. The Dirichlet and Robin boundary conditions are considered. The approximate solution on each time layer is sought as series over basis functions which are taken in the form of the tensor products of cubic B-splines. The coefficients of the series are chosen to satisfy the governing EPDEs in the solution domain. The stability and accuracy of the proposed scheme is demonstrated by several examples. Keywords: Meshless method, Generalized telegraph equation, Nonlinear problem, Cubic B-spline, Crank-Nicolson scheme