A robust and accurate solver for some nonlinear partial differential equations and tow applications

Abstract

Abstract In this paper we introduce a robust and accurate solver in order to solve various classes of nonlinear partial differential equations. This solver gives the closed formula for the solutions. Within this respect, a solver is developed to accurately resolve and represent the complete wave structure of the nonlinear partial differential equations. To verify this solver, the two applications are introduced. The obtained solutions may be applicable for some new observations in physics, fluid mechanics, biology, engineering, economy, astrophysics, meteorological topics, gravitational collapse and laser technology. The theoretical study and obtained solutions reported illustrating that the proposed solver efficient and adequate. The shape for the obtained solutions are illustrated via 2D and 3D plots for suitable values of the free parameters.