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

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 solutio...

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Published inNumerical methods for partial differential equations Vol. 34; no. 5; pp. 1577 - 1597
Main Authors Abu Arqub, Omar, Al‐Smadi, Mohammed
Format Journal Article
LanguageEnglish
Published New York Wiley Subscription Services, Inc 01.09.2018
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ISSN0749-159X
1098-2426
1098-2426
DOI10.1002/num.22209

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Abstract 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.
AbstractList 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.
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 ‐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.
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.
Author Al‐Smadi, Mohammed
Abu Arqub, Omar
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Snippet Recently, many new applications in engineering and science are governed by a series of time‐fractional partial integrodifferential equations, which will lead...
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SubjectTerms 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
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Title Numerical algorithm for solving time‐fractional partial integrodifferential equations subject to initial and Dirichlet boundary conditions
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