In this paper, we investigate a generalization of the Adams-Bashforth method by using the Taylor’s series. In case of m-step method, the local truncation error can be expressed in terms of m − 1 coefficients. With an appropriate choice of coefficients, the proposed method has produced much smaller error than the original Adams-Bashforth method. As an application of the generalized Adams-Bashfor...

In this paper, we propose new variants of the two-step Adams-Bashforth and the one-step Adams-Moulton methods for the numerical integration of ordinary differential equations (ODEs). The methods are constructed geometrically from an exponentially fitted osculating parabola. The accuracy and stability of the proposed variants is discussed and their applicability to some initial value problems is...

By adding a suitable real function on both sides of the quadratic Riccati differential equation, we propose a weighted type of Adams-Bashforth rules for solving it, in which moments are used instead of the constant coefficients of Adams-Bashforth rules. Numerical results reveal that the proposed method is efficient and can be applied for other nonlinear problems.

Semi-implicit multistep methods are an efficient tool for solving large-scale ODE systems. This recently emerged technique is based on modified Adams–Bashforth–Moulton (ABM) methods. In this paper, we introduce new semi-explicit and semi-implicit predictor–corrector the backward differentiation formula Adams–Bashforth We provide a thorough study of numerical stability performance compare their ...

How far the stability domain of a numerical method for approximating solutions to differential equations extends along the imaginary axis indicates how useful the method is for approximating solutions to wave equations; this maximum extent is termed the stability ordinate, also known as the imaginary stability boundary. It has previously been shown that exactly half of Adams-Bashforth, Adams-Mo...

The numerical solution of a variable-order fractional financial system is calculated by using the Adams-Bashforth-Moulton method. The derivative is defined in the Caputo variable-order fractional sense. Numerical examples show that the Adams-Bashforth-Moulton method can be applied to solve such variable-order fractional differential equations simply and effectively. The convergent order of the ...

We consider the weak analogues of certain strong stochastic numerical schemes considered in [10], namely a Adams-Bashforth scheme and a semi-implicit leapfrog scheme. We show that the weak version of the Adams-Bashforth scheme converges weakly with order 2, and the weak version of the semi-implicit leapfrog scheme converges weakly with order 1. We also note that the weak schemes are computation...

in this paper, the (m+1)-step adams-bashforth, adams-moulton, and predictor-correctormethods are used to solve rst-order linear fuzzy ordinary dierential equations. the conceptsof fuzzy interpolation and generalised strongly dierentiability are used, to obtaingeneral algorithms. each of these algorithms has advantages over current methods. moreover,for each algorithm a convergence formula can b...

A numerical method for a class of forward-backward stochastic differential equations (FBSDEs) is proposed and analyzed. The method is designed around the Four Step Scheme (Douglas-Ma-Protter, 1996) but with a Hermite-spectral method to approximate the solution to the decoupled quasilinear PDE on the whole space. A rigorous synthetic error analysis is carried out for a fully discretized scheme, ...