Space time localized scheme to solve some partial integro-differential equations

Iranian Journal of Numerical Analysis and Optimization

مقالات آماده انتشار، پذیرفته شده، انتشار آنلاین از تاریخ 06 اردیبهشت 1404

نوع مقاله: Research Article

شناسه دیجیتال (DOI): 10.22067/ijnao.2025.92731.1617

نویسندگان

Mohammed Hamaidi^* ؛ Mabrouk Briki؛ Ahmed Nouara؛ Brahim Hamdi

Department of Mathematics, Faculty of Exact Sciences and Computer Science, Ziane Achour University, Djelfa, Algeria.

چکیده

It has been demonstrated that the space-time localized radial basis functions collocation method has very good accuracy in several research studies. In this paper, we extend the method to solve the partial integro-differential equations. Since the unknowns of the localized scheme are the values of the interpolated function, the method can be easily combined with the trapezoidal rule to find the numerical solution. The main advantages of such formulation are:  the time discretization is not applied, the time stability analysis is not discussed, and the recomputation of the resulting matrix at each time level is avoided because the matrix is computed once. Different examples are solved to show the accuracy of such a method.

کلیدواژه‌ها

Partial integro-differential equation؛ Localized radial basis functions؛ Space-time scheme؛ Collocation method؛ Trapezoidal rule