Ordinary Hybrid Finite Difference Methods for Solving Burgers’ Equation.
Keywords:
Burgers’ Equation, Crank-Nicholson; Lax-Friedrichs’; Du Fort and Frankel methods.Abstract
Burgers’ equation appears as a model in turbulence and gas dynamics. We construct hybrid finite difference schemes from ordinary finite difference methods for solving this equation. Among the hybrid methods developed are the Crank-Nicholson-Du Fort and Frankel and Crank-Nicholson- Lax-Friendrich’s and Du Fort and Frankel. We determine that the Du Fort and Frankel discretization have an improvement effect on other finite difference schemes whereas the Lax- Friedrich’s method reduces their efficacy. We note that the Du Fort and Frankel method increases the number of grid points involved by one. The increase of the grid points is responsible for the improved accuracy of the Crank-Nicholson and the Hybrid Crank-Nicholson-Lax-Friedrich’s, methods. The hybrid Crank-Nicholson-Lax-Friedrich’s,-Du Fort and Frankel scheme is the most accurate.
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