A Numerical Technique to Solve Time-Fractional Delay Diffusion Wave Equation via Trigonometric Collocation Approach

Abstract

This work demonstrates a numerical scheme comprising the Crank-Nicolson difference scheme in the temporal direction and cubic-trigonometric splines in the spatial direction for solving the time-fractional damped convection-diffusion wave delay differential equation. This equation involves the reaction and damping term and the delay parameter applied in time in the reaction term. This type of delay differential equation was not explored earlier, so we present a numerical scheme that is second-order convergent in the spatial direction and

(3-\alpha )

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order of accuracy in the temporal direction. The proposed method is proved to be unconditionally stable and convergent through rigorous analysis. Two test examples are solved to validate our theoretical findings and manifest the proficiency of the present numerical scheme.

Keywords

Caputo derivative / Cubic trigonometric B-splines / Crank-Nicolson scheme / Stability / Convergence

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Shanghai University