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Numerical solution of Burgers' equation with modified cubic B-spline differential quadrature method

机译：修正三次B样条微分求积法求解Burgers方程的数值解

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摘要

In this paper, a new numerical method, "modified cubic-B-spline differential quadrature method (MCB-DQM)" is proposed to find the approximate solution of the Burgers' equation. The modified cubic-B-spline basis functions are used in differential quadrature to determine the weighting coefficients. The MCB-DQM is used in space, and the optimal four-stage, order three strong stability-preserving time-stepping Runge-Kutta (SSP-RK43) scheme is used in time for solving the resulting system of ordinary differential equations. To check the efficiency and accuracy of the method, four examples of Burgers' equation are included with their numerical solutions, L2 and L1 errors and comparisons are done with the results given in the literature. The proposed method produces better results as compared to the results obtained by almost all the schemes available in the literature, and approaching to the exact solutions. The presented method is seen to be easy, powerful, efficient and economical to implement as compared to the existing techniques for finding the numerical solutions for various kinds of linearonlinear physical models.
机译：本文提出了一种新的数值方法，即“改进的三次B样条微分求积法（MCB-DQM）”，以找到Burgers方程的近似解。修改后的三次B样条基函数在微分正交中用于确定加权系数。 MCB-DQM在空间中使用，并且及时使用最优的四级，三阶强保持稳定性的时间步长Runge-Kutta（SSP-RK43）方案来求解所得的常微分方程组。为了检查该方法的效率和准确性，在其数值解中包括了Burgers方程的四个示例，L2和L1误差，并与文献中给出的结果进行了比较。与通过文献中几乎所有可用方案获得的结果相比，所提出的方法产生了更好的结果，并且接近于精确的解决方案。与为各种线性/非线性物理模型寻找数值解的现有技术相比，所提出的方法被认为易于实施，功能强大，高效且经济。

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