Numerical Strategies for the System of First Order IVPs Using Block Hybrid Extended Trapezoidal Multistep Method of Second Kind for Stiff ODEs

Abstract

A Modified ThreeStep Block Hybrid Extended Trapezoidal Multistep Method of Second Kind (BHETR 2 s) with two off-grid points, one at interpolation and another at collocation point yielding uniform order six (6,6,6,6,6) T for the Numerical Integration of initial value problems of stiff Ordinary Differential Equations was developed. The main method and additional equations were obtained from the same continuous formulation through interpolation and collocation procedures. The stability properties of the method was discussed and from the stability region obtained, the method is suitable for the solution Stiff Ordinary Differential Equations. Three numerical examples were considered to illustrate the efficiency and accuracy.