Abstract
The objective of this paper is to present an efficient numerical technique for solving time fractional modified anomalous subdiffusion equation. Anomalous diffusion equation has its role in various branches of biological sciences. B-spline is a piecewise function to draw curves and surfaces, which maintain its degree of smoothness at the connecting points. B-spline provides an active process of approximation to the limit curve. In current attempt, B-spline curve is used to approximate the solution curve of time fractional modified anomalous subdiffusion equation. The process is kept simple involving collocation procedure to the data points. The time fractional derivative is approximated with the discretized form of the Riemann-Liouville derivative. The process results in the form of system of algebraic equations, which is solved using a variant of Thomas algorithm. In order to ensure the convergence of the procedure, a valid method named Von Neumann stability analysis is attempted. The graphical and tabular display of results for the illustrated examples is presented, which stamped the efficiency of the proposed algorithm.
Highlights
The current study deals with the investigation of modified fractional anomalous subdiffusion equation using hybrid Bspline-based collocation method
Modified fractional anomalous subdiffusion equation have not been solved by hybrid B-spline collocation method yet
A B-spline collocation method is utilized to find the numerical approximation to the solution curve of fractional form of
Summary
The current study deals with the investigation of modified fractional anomalous subdiffusion equation using hybrid Bspline-based collocation method. In another paper by Mohebbi et al [11], the solution of 2D modified anomalous subdiffusion equation was proposed, and this method was based on radial basis functions. Hashmi et al [17, 18] has solved Hunter Saxton equation and space fractional PDE by cubic trigonometric and hybrid B-spline method. The numerical solution of time-space fractional PDEs using B-spline wavelet method is presented by Kargar and Saeedi [19]. Numerical formulation of the Riemann-Liouville derivative for anomalous subdiffusion equation described by Dehghan et al [20] is used as time fractional derivative which is given as. Modified fractional anomalous subdiffusion equation have not been solved by hybrid B-spline collocation method yet.
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