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Abstract
In this paper, a new hybrid approach based on sixth-order finite difference and seventh-order weighted essentially non-oscillatory finite difference scheme is proposed to capture numerical simulation of the regularized long wave-Burgers equation which represents a balance relation among dissipation, dispersion and nonlinearity. The corresponding approach is implemented to the spatial derivatives and then MacCormack method is used for the resulting system. Some test problems discussed by different researchers are considered to apply the suggested method. The produced results are compared with some earlier studies, and to validate the accuracy and efficiency of the method, some error norms are computed. The obtained solutions are in good agreement with the literature. Furthermore, the accuracy of the method is higher than some previous works when some error norms are taken into consideration.
Highlights
In describing many models in a great deal of fields of science, nonlinear partial differential equations (PDEs) play a significant role
One of the popular nonlinear partial differential equations studied for its numerical solutions is the regularized long waveBurgers (RLW-Burgers) equation known as Benjamin-Bona-Mahony-Burgers (BBMB) equation
Investigating an effective and accurate numerical method encourages us to produce a new hybrid approach based on some high order finite difference (FD) schemes for analyzing the behavior of the RLW-Burgers equation
Summary
The subscripts t and x are time and space derivatives, and denote the horizontal coordinate along the channel and the elapsed time, respectively. (x) is a known function as initial condition, is a positive constant, and g u is a C2 smooth nonlinear function. Investigating an effective and accurate numerical method encourages us to produce a new hybrid approach based on some high order finite difference (FD) schemes for analyzing the behavior of the RLW-Burgers equation. One of these FD schemes is a seventh-order weighted essentially non-oscillatory (WENO7) [10, 11, 16] method. Some researchers have combined the WENO schemes with a high order method to overcome some drawbacks [17,18,19] Inspired by these drawbacks in the corresponding studies, we prefer to. The last section includes the summary of findings in the paper
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