The Formation of Implicit Second Order Backward Difference Adam’s Formulae for Solving Stiff Systems of First Order Initial Value Problems of Ordinary Differential Equations

The formation of implicit second order backward difference Adam’s formulae for solving stiff systems of ODEs was study in this paper. We used interpolation and collocation in deriving backward differentiae Adam’s formulae. The basic properties of our method was analyzed, and it was found to be consistent, zero-stability and convergent, we further plotted the region of absolute stability and it was shown to be A-stable. Numerical evidences shows that the multistep method develop is very effective method for in handling linear ODEs either initial value problems or boundary value problems.

CONSTRUCTION OF EFFICIENT GENERAL LINEAR METHODS FOR NON-STIFF DIFFERENTIAL SYSTEMS

This paper describes the construction of explicit general linear methods in Nordsieck form with inherent quadratic stability and large areas of the stability region. After satisfying order and inherent quadratic stability conditions, the remaining free parameters are used to find the methods with large area of region of absolute stability. Examples of methods with p = q + 1 = s = r and p = q = s = r - 1 up to order 6 are given.

3-Point Block Methods for Direct Integration of General Second-Order Ordinary Differential Equations

A Multistep collocation techniques is used in this paper to develop a 3-point explicit and implicit block methods, which are suitable for generating solutions of the general second-order ordinary differential equations of the form . The derivation of both explicit and implicit block schemes is given for the purpose of comparison of results. The Stability and Convergence of the individual methods of the block schemes are investigated, and the methods are found to be 0-stable with good region of absolute stability. The 3-point block schemes derived are tested on standard mechanical problems, and it is shown that the implicit block methods are superior to the explicit ones in terms of accuracy.