Generalized Cash-type Second Derivative Extended Backward Differentiation Formulas for Stiff systems of ODEs

Extended backward differentiation

Abstract

In this paper, a generalized Cash-type second derivative extended backward differentiation formulas (GCE2BD)
is developed as boundary value methods (BVMs) for the numerical solution of stiff systems of ordinary differential
equations (ODEs). The proposed class of methods is O_v,(k+1)-v-stable and A_v,(k+1)-v-stable with (v,(k+1)-v)-boundary
conditions and order k+3 for all values of the step-length k >= 1.The class of methods proposed is exceptional for
the numerical solution of stiff systems whose Jacobians have some relatively large eigenvalues near the imaginary
axis. The accuracy and efficiency of the constructed methods are examined in some details via the numerical
experiments carried out on some well-known linear and non-linear stiff systems using the boundary value techniques
such that the numerical solution of a problem is obtained simultaneously on the entire interval of integration.
The new class of methods is found to compare favorably with existing standard methods in the literature.