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...

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...

Transient stability-constrained optimal power flow (TSCOPF) models comprehensively analyze the security and economic operation of systems. However, they require a high computational effort can suffer from convergence problems when applied to large This study analyzes performance eleven numerical integration algorithms ordinary differential equations that represent system dynamics in TSCOPF mode...

A multistep method with matricial coefficients is developed. It can be used to solve stiff initial value problems of the form y’= Ay + g(x,y). This method bears the nature of the classical Adams-Bashforth-Moulton PC formula and can be shown to be consistent, convergent and A-stable. A careful reformulation of this method legitimatizes the implementation of this algorithm in a variable-step vari...

In this paper numerical studies for the variable-order fractional delay differential equations are presented. Adams-Bashforth-Moulton algorithm has been extended to study this problem, where the derivative is defined in the Caputo variable-order fractional sense. Special attention is given to prove the error estimate of the proposed method. Numerical test examples are presented to demonstrate u...

In this paper, we introduce a new parameter iteration method (P-Iteration for short) ,which can be applied on Adams-Moulton methods to solve initial value problems. Compared with Jacobi iteration method, it has three advantages: (1) it may significantly implement the stable region of the iterative process such that we can efficiently use the large stable region of implicit formula; (2) it allow...

Downward continuation is a key technique for processing and interpreting gravity anomalies, as it has major role in reducing values to horizontal planes identifying small shallow sources. However, can be unstable inaccurate, particularly when depth increases. While the Milne Adams–Bashforth methods based on numerical solutions of mean-value theorem have partly addressed these problems, more acc...