RBF-Based Local Meshless Method for Fractional Diffusion Equations

Abstract

The fractional diffusion equation is one of the important recent models that can efficiently characterize various complex diffusion processes, such as in inhomogeneous or heterogeneous media or in porous media. This article provides a method for the numerical simulation of time-fractional diffusion equations. The proposed scheme combines the local meshless method based on a radial basis function (RBF) with Laplace transform. This scheme first implements the Laplace transform to reduce the given problem to a time-independent inhomogeneous problem in the Laplace domain, and then the RBF-based local meshless method is utilized to obtain the solution of the reduced problem in the Laplace domain. Finally, Stehfest’s method is utilized to convert the solution from the Laplace domain into the real domain. The proposed method uses Laplace transform to handle the fractional order derivative, which avoids the computation of a convolution integral in a fractional order derivative and overcomes the effect of time-stepping on stability and accuracy. The method is tested using four numerical examples. All the results demonstrate that the proposed method is easy to implement, accurate, efficient and has low computational costs.

Parametric Poisson Bifurcated Autoregressive Process: Application to Worldwide, Regional, and Peculiar Countries’ of Automobile Production

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Existence, uniqueness, and galerkin shifted Legendre's approximation of time delays integrodifferential models by adapting the Hilfer fractional attitude

“…It is a relatively new field of study that has gained significant attention from researchers because of its wide-ranging applications in different sectors of science and engineering [ [1] , [2] , [3] , [4] , [5] ]. This has resulted in the development of new mathematical tools and techniques that have been used to solve complex problems in physics, engineering, finance, and other fields [ [6] , [7] , [8] , [9] , [10] ]. Studying fractional calculus has yielded the maturation of numerous numerical strategies for solving fractional models, including Riemann, Caputo, and Grunwald-Letnikov's approaches [ [11] , [12] , [13] ].…”

Haar wavelet based numerical technique for the solutions of fractional advection diffusion equations

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