Abstract
AbstractIn this paper, a residual power series method (RPSM) is combining Taylor’s formula series with residual error function, and is investigated to find a novel analytical solution of the coupled strong system nonlinear Boussinesq-Burgers equations according to the time. Analytical solution was purposed to find approximate solutions by RPSM and compared with the exact solutions and approximate solutions obtained by the homotopy perturbation method and optimal homotopy asymptotic method at different time and concluded that the present results are more accurate and efficient than analytical methods studied. Then, analytical simulations of the results are studied graphically through representations for action of time and accuracy of method.
Highlights
We consider the generalized Boussinesq–Burgers equations given by ut + auux + bwx = 0 wt + c(uw)x + duxxx = 0, where a, b, c, and d are real nonzero constants. (1.1) (1.2)The systems of nonlinear equations are known to describe a wide variety of phenomena in physics, engineering, applied mathematics, chemistry, and biology.The Boussinesq–Burgers equations arise in the study of fluid flow and describe the propagation of shallow water waves
Many phenomena in the world was described by nonlinear partial differential equations that can be solved numerically
In recent years some works have been done in order to find the numerical solution of this equation
Summary
Many phenomena in the world was described by nonlinear partial differential equations that can be solved numerically. Boussinesq–Burgers equation is one of the famous nonlinear equations. Author solved Boussinesq–Burgers equations numerically by novel and new method called residual power series method (RPSM). The author compared the present work via two another published method and concluded that the present results are more accurate and efficient than analytical methods studied. Action of time and accuracy of the method was studied graphically at last
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