Abstract
By coupling of radial kernels and localized Laplace transform, a numerical scheme for the approximation of time fractional anomalous subdiffusion problems is presented. The fractional order operators are well suited to handle by Laplace transform and radial kernels are also built for high dimensions. The numerical computations of inverse Laplace transform are carried out by contour integration technique. The computation can be done in parallel and no time sensitivity is involved in approximating the time fractional operator as contrary to finite differences. The proposed numerical scheme is stable and accurate.
Highlights
In the last decades, many researchers have studied the fractional calculus [1,2,3]
An implicit meshless technique based on the radial basis functions for the numerical simulation of the anomalous subdiffusion equation can be found in [25]. e convergence and stability of these mesh-free methods can be found in [26, 27]. ese globally defined RBF methods cause illcondition system matrices [28]
To avoid the issues of computational efficiency and instability of the system matrix, we introduce a new technique Laplace transform-based local RBF method in solving the time fractional modified anomalous subdiffusion equations in irregular domain
Summary
Many researchers have studied the fractional calculus [1,2,3]. Differential equations of fractional order have many applications in the field of science and engineering [4,5,6,7]. Analytical solution of many fractional differential equations is not possible or very hard to find, so we need a new numerical technique to find its approximate solution. RBF-based methods were used in solving fractional partial differential equations (FPDEs) [22,23,24]. An implicit meshless technique based on the radial basis functions for the numerical simulation of the anomalous subdiffusion equation can be found in [25]. Laplace transform is combined with RBF method in [32, 33]. To avoid the issues of computational efficiency and instability of the system matrix, we introduce a new technique Laplace transform-based local RBF method in solving the time fractional modified anomalous subdiffusion equations in irregular domain. Respectively, where α, β ∈ (0, 1), t ∈ [0, T], ]1, ]2 are positive constants, Δ is the Laplace operator, and f(x, t) is some given function
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