An efficient algorithm combining an optimized hybrid block method and the differential quadrature method for solving Hunter–Saxton equation

Abstract

AbstractIn this paper, the numerical solution of a mixed derivative type Hunter–Saxton equation is addressed. A given equation is discretized transforming it into a system of ODEs with the use of a cubic trigonometric B-splines based differential quadrature method. The system is further solved using a fifth-order optimized one-step hybrid block method. Three numerical illustrations validate the efficiency of the proposed scheme and show its better performance through very accurate results. Stability and convergence analysis are also performed.