Abstract
A class of high order extended boundary value methods (HEBVMs) suitable for the numerical approximation of stiff systems of ordinary differential equations (ODEs) is constructed. This class of BVMs is based on the second derivative class of linear multistep formulas (LMF) and it provides a set of very highly stable methods that can produce considerably accurate solutions to stiff systems whose Jacobians have some large eigenvalues lying close to the imaginary axis. The class of BVMs derived herein is of high order, small error constants and large region of absolute stability. Specifically, it is O-k1,O- k2-stable, A(k1, k2)-stable with (k(1), k(2))-boundary conditions and order p = k + 4 for values of the step length k >= 1. The numerical results obtained from standard linear and non-linear stiff systems indicate that this scheme is highly competitive with existing methods. (C) 2021 Elsevier B.V. All rights reserved.
NSTL
Elsevier