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

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.