Cubic B-splines collocation method for solving a partial integro-differential equation with a weakly singular kernel

نویسندگان
Gholamian, Mohammad ID 1
Saberi-Nadjafi, Jafar ID 2
Soheili, Ali Reza ID 3

1 Department of Applied Mathematics, Faculty of Mathematical Sciences, Ferdowsi University of Mashhad, International Campus, Mashhad, Iran

2 Department of Applied Mathematics, Faculty of Mathematical Sciences, Ferdowsi University of Mashhad, International Campus, Mashhad, Iran

3 Department of Applied Mathematics, Faculty of Mathematical Sciences, Ferdowsi University of Mashhad, International Campus, Mashhad, Iran

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چکیده

In this paper, we apply a numerical scheme for the solution of a second order partial integro-differential equation with a weakly singular kernel. In the time direction, the backward Euler method time-stepping is used to approximate the differential term and the cubic B-splines is applied to the space discretization. Detailed discrete schemes, the convergence and the stability of the method is demonstrated. Next, the computational efficiency and accuracy of the method are examined by the numerical results.

کلیدواژه‌ها
Cubic B-splines, Partial integro-differential equation, Backward Euler method