Parallel Initial-Value Algorithm for Quasilinear Shock Problems with Turning Points

Abstract

In this paper, a parallel initial value algorithm is presented for quasilinear stationary shock problems with turning points exhibiting two-boundary layers or an internal layer. The method is based on obtaining two independent asymptotically equivalent first-order singularly-perturbed initial-value problems (SPIVPs) of the original problem. The error is estimated to be of order ε . The two SPIVPs are modified to obtain two boundary-layer correction problems. These non-stiff initial-value problems are solved simultaneously in parallel process using (RKV45) non-stiff code integrator. The obtained solutions are combined to approximate the solution of the original problem. Numerical experiments indicate the high accuracy and the efficiency of the method. Furthermore, the accuracy of numerical results improves as the small parameter ε tends to zero Keywords: quasilinear singular perturbation problems; turning points problems; two boundary layer; internal layer; Initial value methods, parallel algorithms.