Approximate solution of time-fractional non-linear parabolic equations arising in Mathematical Physics
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Date
2024-05-31
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Nigerian Society of Physical Sciences
Abstract
In this paper, we studied and analysed a new iterative method for solving time-fractional non-linear equations by obtaining approximate solutions to
the Allen-Cahn, Newell-Whitehead, and Fisher equations by putting the parameter α = 1 and varying the values of γ, ψ, and τ. These three equations
were derived from the general non-linear dynamical wave equations when the constants therein assumed certain specific values. Obviously, from
the tabulated results, we observed that the approximate solution for each example compares favourably with the existing results in the literature;
therefore, the proposed scheme is effective and accurate in solving Allen-Cahn, Newell-Whitehead, and Fisher equations. All the computational
work was done using Mathematica, and all the graphs were plotted using MATLAB.