A New Method for Numerical Solution of the Fractional Relaxation and Subdiffusion Equations Using Fractional Taylor Polynomials
For researchers solving fractional differential equations, this method offers improved accuracy but is incremental, building on existing polynomial-based approaches.
The authors propose a method using fractional Taylor polynomials to improve the accuracy of numerical solutions for fractional relaxation and subdiffusion equations, addressing singularities at the initial point.
The accuracy of the numerical solution of a fractional differential equation depends on the differentiability class of the solution. The derivatives of the solutions of fractional differential equations often have a singularity at the initial point, which may result in a lower accuracy of the numerical solutions. We propose a method for improving the accuracy of the numerical solutions of the fractional relaxation and subdiffusion equations based on the fractional Taylor polynomials of the solution at the initial point.