AN EFFICIENT NUMERICAL SCHEME FOR BURGERS-EQUATION

This paper applies the multiquadric (MQ) as a spatial approximation sc heme for solving the nonlinear Burgers' equation. For comparison purpo ses, a low order explicit finite difference approximation of the time derivative is employed.By decreasing the time step of the computation, it is shown that the major numerical error is from the time integrati on instead of the MQ spatial approximation; The numerical results indi cate that this MQ offers an excellent approximation for all possible v alues of Reynolds number. An adaptive algorithm is also developed to a djust the MQ interpolation points tb the peak of the shock wave which is shown to provide an improved numerical result.. Numerical compariso ns are made with most of the existing numerical schemes for solving th e Burgers' equation. (C) 1998 Elsevier Science Inc. All rights reserve d.