A Class of A-Stable Order Four and Six Linear Multistep Methods for Stiff Initial Value Problems

Abstract

A new three and five step block linear methods based on the Adams family for the direct solution of stiff initial value problems (IVPs) are proposed. The main methods together with the additional methods which constitute the block methods are derived via interpolation and collocation procedures. These methods are of uniform order four and six for the three and five step methods respectively. The stability analysis of the two methods indicates that the methods are A–stable, consistent and zero stable. Numerical results obtained using the proposed new block methods show that they are attractive for the solutions of stiff problems and compete favorably with the well-known Matlab stiff ODE solver ODE23S.

Keywords: Linear multistep methods, initial value problems, interpolation and collocation.