Fourth-order finite difference method for solving Burgers’ equation. (English) Zbl 1084.65078

The main scope of the article is the elaboration of the two level three-point scheme by means of the method of unknown coefficients for an approximate solving of the nonlinear Burgers’ problem. The local error of this scheme is of second-order by the time-step \(\Delta t\) and of fourth-order by the variable space step \(h\). The present method can be written in matrix form \(AI^{m+1}_{i,j}= BU_{i,j-1}\), where \(A\) is a tridiagonal matrix.
The constructed algorithm is applied to the numerical solution of some concrete problems with different Reynolds numbers. The obtained numerical results are compared with the same results by other known methods. The comparison is made only by numerical results and the main properties of other methods are neglected.


65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs
65M12 Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs
35Q53 KdV equations (Korteweg-de Vries equations)
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