Numerical algorithm for solving time‐fractional partial integrodifferential equations subject to initial and Dirichlet boundary conditions

• Published in: Numerical methods for partial differential equations Vol. 34; no. 5; pp. 1577 - 1597
• Main Authors: Abu Arqub, Omar, Al‐Smadi, Mohammed
• Format: Journal Article
• Language: English
• Published: New York Wiley Subscription Services, Inc 01.09.2018
• Subjects: Algorithms; Boundary conditions; Computer simulation; Dirichlet problem; Error analysis; fractional calculus theory; Infinite series; Iterative algorithms; Iterative methods; Nonlinear equations; Numerical analysis; partial integrodifferential equation; reproducing kernel algorithm; Simulated annealing
• ISSN: 0749-159X; 1098-2426
• DOI: 10.1002/num.22209

Recently, many new applications in engineering and science are governed by a series of time‐fractional partial integrodifferential equations, which will lead to new challenges for numerical simulation. In this article, we propose and analyze an efficient iterative algorithm for the numerical solutions of such equations subject to initial and Dirichlet boundary conditions. The algorithm provide appropriate representation of the solutions in infinite series formula with accurately computable structures. By interrupting the n ‐term of exact solutions, numerical solutions of linear and nonlinear time‐fractional equations of nonhomogeneous function type are studied from mathematical viewpoint. Convergence analysis, error estimations, and error bounds under some hypotheses which provide the theoretical basis of the proposed algorithm are also discussed. The dynamical properties of these numerical solutions are discussed and the profiles of several representative numerical solutions are illustrated. Finally, the utilized results show that the present algorithm and simulated annealing provide a good scheduling methodology to such integrodifferential equations.