ارايه الگوريتم براي تعيين خطاي قطع موضعي، سازگاري و تقليل خطا در روشهاي تفاضلي براي حل عددي معادلات ديفرانسيل با مشتقات جزيي سهموي بدون استفاده از بسط تيلور

An Algorithm for Finding the Local Truncation Error, Consistency, and Error Reducible of the Finite - Difference Methods for the Parabolic PDEs without using the Taylorʹs Expansion

In this paper, we derive a very powerful algorithm for finding the local truncation error of an explicit or implicit finite - difference method to approximate solutions of partial differential equations (PDEs) of parabolic type without using the Taylors expansion. The consistency of the finite - difference schemes to these equations will be shown. Finally, we study a method for the error reducible and to assess its validity and accuracy, the method is applied to solve several test problem.