Combining Cubic B-Spline Galerkin Method with Quadratic Weight Function for Solving Partial Integro-Differential Equations

  • Hameeda O. Al-Humedi Department of Mathematics, College of Education for Pure Sciences, Basrah University, Basrah, Iraq.
  • Zahraa Adnan jameel Department of Mathematics, College of Education for Pure Sciences, Basrah University, Basrah, Iraq.
Keywords: B-spline method,, Galerkin method,, integro-differential equation,, Von-Neuman.

Abstract

In this article, a numerical scheme was implemented for solving the partial integro-differential equations (PIDEs) with weakly singular kernel by using the cubic B-spline Galerkin method with quadratic B-spline as a weight function. backward Euler scheme was used for time direction and the cubic B-spline Galerkin method with quadratic weight function was used for spatial derivative. We observed from the numerical examples that the proposed method possesses a high degree of efficiency and accuracy. In addition, the numerical results are in suitable agreement with the exact solutions via calculating L_2 and〖 L〗_∞ norms errors. Theoretically, we discussed the stable evaluation of the current method using the Von-Neumann method, which explained that the present technique is unconditionally stable.

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Published
2020-02-17
How to Cite
Al-Humedi, H., & jameel, Z. (2020). Combining Cubic B-Spline Galerkin Method with Quadratic Weight Function for Solving Partial Integro-Differential Equations. Journal of Al-Qadisiyah for Computer Science and Mathematics, 12(1), Math Page 9 -. https://doi.org/10.29304/jqcm.2020.12.1.660
Section
Math Articles