Higher-order predictor–corrector methods for fractional Benjamin–Bona–Mahony–Burgers’ equations

Abstract

In this paper, we construct a higher order predictor–corrector technique for time fractional Benjamin–Bona–Mahony–Burgers’ equations. Instead of directly using an explicit scheme as the predictor in traditional predictor–corrector methods, we employ a new predictor scheme based on the author’s previous work ([24] https://doi.org/10.1007/s10910-024-01589-6), in which the given nonlinear equation is linearized by several linearization techniques and solved by Adams–Moulton scheme for the temporal direction and fourth order finite difference scheme for the spatial direction. Once the predictor solution is obtained, the higher order Adams–Moulton method is used as the corrector. Moreover, to make much higher order technique, a multiple correction technique is introduced by repeatedly correcting the results induced from the predictor. Numerical results demonstrate the efficiency of the proposed schemes.