Numerical treatment for the fractional Brusselator system by combination of Laplace transform and Adams fourth-order predictor-corrector methods

Source abstract

Abstract This paper is devoted to introducing an accurate method to solve numerically the fractional Brusselator system (FBS). The proposed technique relies on combining the good features of both the Laplace transform method (LTM) and the Adams fourth-order predictor-corrector method (A4PCM). This technique involves using the Laplace transform and the linear Lagrange interpolation to derive an approximate formula of the fractional Caputo derivatives and use it to convert the FBS into a system of first-order ordinary differential equations (ODEs) and then solving these equations numerically by applying the A4PCM. The convergence and error estimations for the suggested scheme are also included by presenting the stability analysis as well as computing the order of convergence. Numerical examples illustrate the good impact of the strategies and rightness of the theoretical framework of the suggested method with high accuracy. One of the advantages of this proposed technique is its ability to provide a highly accurate numerical solution to the model under study over time intervals larger than one (as is the case with most analytical methods). Furthermore, using the proposed fractional derivative approximation eliminates the need to maintain the complete time history of the solution, resulting in a simpler and easier-to-use time-domain model.