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A numerical scheme based on differential quadrature method to solve time dependent Burgers' equation

机译：基于微分求积法求解与时间有关的Burgers方程的数值方案

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摘要

Purpose - The purpose of this paper is to propose a numerical method to solve time dependent Burgers' equation with appropriate initial and boundary conditions. Design/methodology/approach - The presence of the nonlinearity in the problem leads to severe difficulties in the solution approximation. In construction of the numerical scheme, quasilinearization is used to tackle the nonlinearity of the problem which is followed by semi discretization for spatial direction using differential quadrature method (DQM). Semi discretization of the problem leads to a system of first order initial value problems which are followed by fully discretization using RK4 scheme. The method is analyzed for stability and convergence. Findings - The method is illustrated and compared with existing methods via numerical experiments and it is found that the proposed method gives better accuracy and is quite easy to implement. Originality/value - The new scheme is developed by using some numerical schemes. The scheme is analyzed for stability and convergence. In support of predicted theory some test examples are solved using the presented method.
机译：目的-本文的目的是提出一种数值方法，以在适当的初始和边界条件下求解与时间相关的Burgers方程。设计/方法/方法-问题中存在非线性会导致解决方案逼近中的严重困难。在数值方案的构造中，使用拟线性化来解决问题的非线性，然后使用差分正交方法（DQM）对空间方向进行半离散化。问题的半离散化导致一阶初值问题的系统，接着是使用RK4方案的完全离散化。分析了该方法的稳定性和收敛性。研究结果-通过数值实验举例说明了该方法，并将其与现有方法进行了比较，发现该方法具有更高的准确性，并且易于实施。创意/价值-通过使用一些数字方案来开发新方案。分析该方案的稳定性和收敛性。为了支持预测理论，使用该方法解决了一些测试示例。

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