A predictor-corrector scheme for the tempered fractional differential equations with uniform and non-uniform meshes

摘要

Tempered fractional derivatives and the corresponding tempered fractional differential equations have played a key role in physical science. In this paper, for solving the tempered fractional ordinary differential equation, the predictor-corrector (PC) methods with uniform and non-uniform meshes of Deng et al. (Numer Algorithms 74(3):717-754, 2017) are developed, by using the piecewise quadratic interpolation polynomial. The error bounds of proposed predictor-corrector schemes with uniform and equidistributing meshes are obtained. We proved that the presented numerical method has a higher-order convergence order O(h(3)). Also, some numerical examples are constructed to demonstrate the efficacy and usefulness of the numerical methods. Finally, the results of PC schemes with uniform and non-uniform given in Deng et al. (2017) and presented schemes (improved PC with uniform and non-uniform meshes) are compared for different values of parameters.