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- Title
Application of Asymptotic Homotopy Perturbation Method to Fractional Order Partial Differential Equation.
- Authors
Gul, Haji; Ali, Sajjad; Shah, Kamal; Muhammad, Shakoor; Sitthiwirattham, Thanin; Chasreechai, Saowaluck
- Abstract
In this article, we introduce a new algorithm-based scheme titled asymptotic homotopy perturbation method (AHPM) for simulation purposes of non-linear and linear differential equations of non-integer and integer orders. AHPM is extended for numerical treatment to the approximate solution of one of the important fractional-order two-dimensional Helmholtz equations and some of its cases. For probation and illustrative purposes, we have compared the AHPM solutions to the solutions from another existing method as well as the exact solutions of the considered problems. Moreover, it is observed that the symmetry or asymmetry of the solution of considered problems is invariant under the homotopy definition. Error estimates for solutions are also provided. The approximate solutions of AHPM are tabulated and plotted, which indicates that AHPM is effective and explicit.
- Subjects
PARTIAL differential equations; NONLINEAR differential equations
- Publication
Symmetry (20738994), 2021, Vol 13, Issue 11, p2215
- ISSN
2073-8994
- Publication type
Article
- DOI
10.3390/sym13112215