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FAST O(N) HYBRID METHOD FOR THE SOLUTION OF TWO DIMENSIONAL TIME FRACTIONAL CABLE EQUATION

Fouad Mohammad Salama, Norhashidah Hj. Mohd Ali

Abstract


It is time and memory consuming when numerically solving time fractional differential equations as it requires O(N^2) computational cost and O(NM) memory complexity. N and M are the total number of time levels and space grid points, respectively. In this paper, we present an efficient hybrid method with O(N) computational cost and O(M) memory complexity in solving the two-dimensional time fractional cable equation. The Laplace transform method and implicit finite difference scheme are used to derive the hybrid method. The stability of the numerical scheme has been carried out. Numerical results show that the hybrid method compares well with the exact solution and performs faster compared to a standard finite difference scheme.

Keywords


Fractional cable equation; Caputo fractional derivative; Laplace transform; Finite difference scheme; Stability.

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DOI: http://dx.doi.org/10.6084/ijact.v8i11.1014

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