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

Document Type : Original Article

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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 orderε . 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

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