Computational algorithm for solving singular Fredholm time-fractional partial integrodifferential equations with error estimates

In this article, we propose and analyze an efficient computational algorithm for the numerical solutions of singular Fredholm time-fractional partial integrodifferential equations subject to Dirichlet functions type. The algorithm provide appropriate representation of the solutions in infinite serie...

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Veröffentlicht in:Journal of applied mathematics & computing Jg. 59; H. 1-2; S. 227 - 243
1. Verfasser: Abu Arqub, Omar
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Berlin/Heidelberg Springer Berlin Heidelberg 15.02.2019
Springer Nature B.V
Schlagworte:
Algorithms
Applied mathematics
Computational Mathematics and Numerical Analysis
Computer simulation
Dirichlet problem
Error analysis
Infinite series
Mathematical and Computational Engineering
Mathematics
Mathematics and Statistics
Mathematics of Computing
Nonlinear equations
Original Research
Simulated annealing
Theory of Computation
Fredholm operator
Reproducing kernel algorithm
Fractional calculus theory
Singular partial integrodifferential equation
ISSN:1598-5865, 1865-2085
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Zusammenfassung:In this article, we propose and analyze an efficient computational algorithm for the numerical solutions of singular Fredholm time-fractional partial integrodifferential equations subject to Dirichlet functions type. 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.
Bibliographie:ObjectType-Article-1
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ISSN:1598-5865
1865-2085
DOI:10.1007/s12190-018-1176-x