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A computational method for time fractional partial integro-differential equations

Mojahedfar M., Tari Abolfazl, Shahmorad S.

Journal of Applied Analysis

2020

Vol. 26, nr 2

315--323

In this paper, a class of time fractional partial integro-differential equations (FPIDEs) with initial conditions is studied. Some operational matrices are used to reduce a FPIDE problem to a system of algebraic equations with special properties. The resulted system is solved to give an approximate solution to the problem. Error estimation is also discussed for the approximate solution. Finally, some numerical examples are given to show the accuracy of the proposed method.

Convergence analysis of piecewise continuous collocation methods for higher index integral algebraic equations of the Hessenberg type

Shiri B., Shahmorad S., Hojjati G.

International Journal of Applied Mathematics and Computer Science

2013

Vol. 23, no. 2

341--355

In this paper, we deal with a system of integral algebraic equations of the Hessenberg type. Using a new index definition, the existence and uniqueness of a solution to this system are studied. The well-known piecewise continuous collocation methods are used to solve this system numerically, and the convergence properties of the perturbed piecewise continuous collocation methods are investigated to obtain the order of convergence for the given numerical methods. Finally, some numerical experiments are provided to support the theoretical results.