A Family of Implicit Uniformly Accurate Order Block Integrators for the Solution of y" =f(x,y,y¹)

Abstract

We consider a family of four, five and six-step block methods for the numerical integration of ordinary differential equations of the type y= f(x, y, y¹). The main methods and their additional equations are obtained from the same continuous formulation via interpolation and collocation procedures. The methods which are all implicit are of uniform order and are assembled into a single block equations. These equations which are self starting are simultaneously applied to provide for y₁, y₂, …, yĸ at once without recourse to any Predictors for the Ordinary differential equations. The order of accuracy, convergence analysis and absolute stability regions of the block methods are also presented.