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Finite Difference Method with Metaheuristic Orientation for Exploration of Time Fractional Partial Differential Equations

This exposition deals with the implementation of a robust nature inspired metaheuristic technique for computing the approximate solutions of Caputo type nonlinear time fractional partial differential equations (PDEs) in an effective and fruitful manner. The proposed finite difference metaheuristic s...

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Bibliographic Details
Published in:International journal of applied and computational mathematics 2021-08, Vol.7 (4), Article 121
Main Authors: Khan, Najeeb Alam, Ahmed, Samreen
Format: Article
Language:English
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Summary:This exposition deals with the implementation of a robust nature inspired metaheuristic technique for computing the approximate solutions of Caputo type nonlinear time fractional partial differential equations (PDEs) in an effective and fruitful manner. The proposed finite difference metaheuristic solver (FDMS) comprises the fourfold procedure of Laplace transformation, approximation via finite difference scheme, fabrication of the global residue function in the root mean square sense and finally the optimization of the constructed residue function by utilization of three distinct nature inspired metaheuristic techniques, which belongs to the physics, evolution and the swarm based categories. The offered FDMS is benchmarked on some well-known and extensively used time fractional PDEs. The computed results are compared with the available exact solution and some former numerical and metaheuristic techniques, which expounds the correctness and accuracy of the suggested technique. Detailed performance analysis is carried out to perform an in-depth investigation and examination of the proposed design methodology in terms of accuracy, convergence and consistency. Moreover, statistical inference is drawn on the basis of large independent runs of the projected metaheuristic algorithm. The results of statistical parameters in terms of mean, standard deviation and mean deviation that are calculated on the basis of hundred independent runs certifies the functionality and reliability of the recommended technique.
ISSN:2349-5103
2199-5796
DOI:10.1007/s40819-021-01061-y