Habib, H., El-Zahar, E. (2008). Parallel Initial-Value Algorithm for Quasilinear Shock Problems with Turning Points. The International Conference on Mathematics and Engineering Physics, 4(International Conference on Mathematics and Engineering Physics (ICMEP-4)), 1-12. doi: 10.21608/icmep.2008.29852

H. M. Habib; E. R. El-Zahar. "Parallel Initial-Value Algorithm for Quasilinear Shock Problems with Turning Points". The International Conference on Mathematics and Engineering Physics, 4, International Conference on Mathematics and Engineering Physics (ICMEP-4), 2008, 1-12. doi: 10.21608/icmep.2008.29852

Habib, H., El-Zahar, E. (2008). 'Parallel Initial-Value Algorithm for Quasilinear Shock Problems with Turning Points', The International Conference on Mathematics and Engineering Physics, 4(International Conference on Mathematics and Engineering Physics (ICMEP-4)), pp. 1-12. doi: 10.21608/icmep.2008.29852

Habib, H., El-Zahar, E. Parallel Initial-Value Algorithm for Quasilinear Shock Problems with Turning Points. The International Conference on Mathematics and Engineering Physics, 2008; 4(International Conference on Mathematics and Engineering Physics (ICMEP-4)): 1-12. doi: 10.21608/icmep.2008.29852

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 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