A new numerical scheme based on Newton polynomial with application to Fractional nonlinear differential equations

Abstract

Very recently, a new numerical scheme was introduced. The numerical scheme was developed using the Newton polynomial, as it is known to be more accurate than the Lagrange polynomial that was used to generate the well-known Adams-Bashforth scheme. The numerical method has been revealed very accurate in both cases classical and fractional differential equations. We further apply in this paper, this new numerical scheme for some chaotic problems to see the stability and access it accuracy.