Application of a Modified Cubic B-spline Differential Quadrature Method to a Class of Nonlinear Hyperbolic PDEs with Nonlocal Boundary Conditions

Authors

  • Raziyeh Mirzahashemi Department of Mathematical Sciences, Yazd University, Yazd, Iran
  • Mohammad Heydari Department of Mathematical Sciences, Yazd University, Yazd, Iran

Keywords:

Nonlinear hyperbolic PDEs, Nonlocal boundary conditions, Modified cubic B-splines, Crank-Nicolson method, Differential quadrature method, Convergence analysis.

Abstract

This paper introduces an efficient numerical method for solving a class of second-order nonlinear hyperbolic PDEs with nonlocal boundary conditions. The proposed approach begins by transforming the governing equation into a system of first-order PDEs. Next, the Crank–Nicolson finite difference method is applied to derive the time semi-discrete formulation of the problem. Subsequently, a fully discrete scheme is developed using an improved cubic B-spline and its corresponding differential quadrature method. The method enables the simultaneous approximation of the solution and its time derivative. The stability and convergence of the time semi-discrete form are rigorously investigated using the energy method. Finally, the accuracy and performance of the proposed method are evaluated through numerical experiments on several test problems, with comparisons made against existing methods in the literature.

Published

2026-08-31

Issue

Vol. 20

Section

Vol. 20, No. 6, (2026)

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