Abstract
A finite difference scheme based on extended cubic B-spline method for the solution of time fractional telegraph equation is presented and discussed. The Caputo fractional formula is used in the discretization of the time fractional derivative. A combination of the Caputo fractional derivative together with an extended cubic B-spline is utilized to obtain the computed solutions. The proposed scheme is shown to possess the unconditional stability property with second order convergence. Numerical results demonstrate the applicability, simplicity and the strength of the scheme in solving the time fractional telegraph equation with accuracies very close to the exact solutions.
Highlights
1.1 Problem statement In this work, we consider the following one dimensional time fractional telegraph equation (TFTE) with reaction term [1]:∂2αu(x, t) ∂αu(x, t) ∂2u(x, t)∂t2α + 2λ ∂tα + μu(x, t) = ν ∂x2 + f (x, t),(x, t) ∈ [a, b] × [0, T] (1)with initial and boundary conditions ⎧⎪⎪⎪⎪⎪⎨uut((xx,00))==f1f2((xx)),⎪⎪⎪⎪⎪⎩uu((ba, t) t) = =
Tasbozan et al [23] developed a numerical solution of fractional diffusion equation via the cubic B-spline collocation method
Yaseen et al [28] presented a scheme for the numerical solution of fractional diffusion equation using a finite difference method based on cubic trigonometric B-spline basis functions
Summary
1.1 Problem statement In this work, we consider the following one dimensional time fractional telegraph equation (TFTE) with reaction term [1]:. Dehghan and Shokri [14] presented a numerical method for solving hyperbolic telegraph equation using collocation points and approximated the solution via thin plate spline radial basic functions. Tasbozan et al [23] developed a numerical solution of fractional diffusion equation via the cubic B-spline collocation method. Akram and Tariq [24] presented a numerical scheme based on the quintic spline collocation method for the solution of fractional boundary value problems. Arshed [26] solved a time fractional super-diffusion fourth order differential equation using the quintic B-spline collocation method. Yaseen et al [28] presented a scheme for the numerical solution of fractional diffusion equation using a finite difference method based on cubic trigonometric B-spline basis functions.
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