Nonlinear dynamics of the Burgers' equation and numerical experiments

Bashan Ali

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Nonlinear dynamics of the Burgers' equation and numerical experiments

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In this study, we have modified quintic B-spline base function to use for numerical solution of the Burgers' equation. For this purpose, the numerical algorithm differential quadrature method and Crank-Nicolson scheme are used for space and time discretization, respectively. To deal with nonlinear terms, they are linearized by using Rubin-Graves technique. To observe the accuracy of the present modification, ten different and important test problems are solved successfully. The present results are compared with earlier single methods and mixed methods to see the efficiency of the present algorithm. All comparisons display that the present approach developed the numerical results according to earlier ones. Numerical simulations are plotted at selected time steps to observe the physical behaviour of the waves in 2D and 3D. The rate of convergence related to space is calculated for different examples and reported with error norms.

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《mathematical sciences》 |2022年第2期|183-205|共23页
作者
Bashan Ali;
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作者单位

Zonguldak Bulent Ecevit Univ;

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正文语种英语
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Burgers#8217; equation; Convergence; Modified quintic B-spline; Differential quadrature method; Finite difference method; DIFFERENTIAL QUADRATURE; COLLOCATION SOLUTION; SHOCK-WAVE; ALGORITHM; APPROXIMATION; SIMULATION; SCHEME;

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机译：Dynamical Approach Study of Spurious Steady-State Numerical Solutions of Nonlinear Differential Equations, Part III. The Effects of Nonlinear Source Terms in Reaction-Convection Equations
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机译：Dynamical Approach Study of Spurious Steady-State Numerical Solutions of Nonlinear Differential Equations Part IV. Stability vs. Methods of Discretizing Nonlinear Source Terms in Reaction-Convection Equations
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Nonlinear dynamics of the Burgers' equation and numerical experiments

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