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

Document Type : Research Article

Authors

• M. Hamaidi
• M. Briki
• A. Nouara
• B. Hamdi

Department of Mathematics, Faculty of exact sciences and computer science, Ziane Achour University, Djelfa, Algeria.

10.22067/ijnao.2025.92731.1617

Abstract

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 as follows: 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. 

Keywords

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

Main Subjects

• Modeling and Simulation

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