A new spline technique for the time fractional diffusion-wave equation

Singh, Suruchi; Singh, Swarn; Aggarwal, Anu G.

doi:10.1016/j.mex.2023.102007

Cited by 3 publications

(1 citation statement)

References 20 publications

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“…A combination of method of lines and spline approximation were used to obtain the numerical solution of space fractional diffusion equation by [7]. A cubic B-spline collocation method was employed to solve time fractional wave equation in [8] and anomalous fractional diffusion equation in [9]. A modified spline collocation was proposed and studied by [10] for linear fractional differential equations.…”

Section: Introductionmentioning

confidence: 99%

Solution of the Space Fractional Diffusion Equation Using Quadratic B-Splines and Collocation on Finite Elements

Adetona,

Parumasur,

Singh

2024

Contemp. Math.

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In this paper, we consider the solution of the space fractional diffusion equation using orthogonal collocation on finite elements (OCFE) with quadratic B-spline basis functions. The main advantage of quadratic B-splines is that they have good interpolating properties and can be easily adapted for solving problems on non-uniform grids. The method is unconditionally stable and its convergence is also discussed. It is of order (3 − α) for 1 < α < 2. We present various linear and nonlinear examples. The solutions compared favourably with previous results in the literature.

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