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In this paper, the solutions of time–fractional Burger’s equation and time–fractional coupled Burgers’ equations are obtained using the parametric quintic spline method with a local truncation error of order eight. Moreover, the stability analysis of the present method is demonstrated using Von–Neumann method. Also, to show the accuracy of this method, some examples with different cases for Burger’s and coupled Burgers’ equations are presented and compared with the previous methods.

In this paper, a new technique for solving the generalized regularized long wave (GRLW) equation is investigated. This technique depends on a combination of the non–polynomial quintic spline method (NPQSM) with the finite difference approximation and Crank–Nicolson scheme. The stability analysis of the present method is concluded using the Von–Neumann method. Also, the most popular three invariants of motion of GRLW equation are obtained for the given problems and their numerical results are compared with the analytical values. In addition, a comparison between the present method and the previous methods and the error norms L2 and L∞ are presented to show the accuracy of the suggested method.

In this paper, the numerical solutions of time fractional Burger’s and coupled Burgers’ equations are obtained using the parametric quintic spline method with a local truncation error of order eight in distance direction. Additionally, the von Neumann method was utilized for studying the stability analysis of the present method. Finally, to show the accuracy of this method, some examples with different cases for Burger’s and coupled Burgers’ equations are presented and their results are compared with the previous methods.