A predictor–corrector scheme for solving nonlinear fractional differential equations with uniform and nonuniform meshes

Abstract

In this paper, we develop two algorithms for solving linear and nonlinear fractional differential equations involving Caputo derivative. For designing new predictor–corrector (PC) schemes, we select the mesh points based on the two equal-height and equal-area distribution. Furthermore, the error bounds of PC schemes with uniform and equidistributing meshes are obtained. Finally, examples are constructed for illustrating the obtained PC schemes with uniform and equidistributing meshes. A comparative study is also presented.