THIRD DERIVATIVE MULTISTEP METHODS WITH OPTIMIZED REGIONS OF ABSOLUTE STABILITY FOR STIFF IVPS IN ODES
Authors: *Athe B.O, Muka K.O
Adam’s type methods are known to be zero-stable by design. The backward differentiation formulas are viewed as the dual of the Adams method because of the structure of their second and third characteristics polynomials. Although they are plagued by zero-instability for large step sizes, they are good integrator for stiff initial value problems in ordinary differential equations. This paper is on the derivation of method which combines the characteristics of Adam’s type methods and the backward differentiation formulas using the methods of collocation and interpolation. Proposed method is A-stable for order p?7 and A(?)-stable for p?12. Numerical examples are presented to show the suitability of method developed in the integration of stiff initial value problems.
Affiliations: Advanced Research Laboratory, Department of Mathematics, Faculty of Physical Sciences, University of Benin, PMB 1154, Benin City, Nigeria
Keywords: Characteristics Polynomials, Region Of Absolute Stability, Adam’s Type, A- Stable, A(?) –stable
Published date: 2017/12/29