Some $A$-stable methods for stiff ordinary differential equations

Abstract:

This paper gives some $A$-stable methods of order $2n$, with variable coefficients, based on Hermite interpolation polynomials, for the stiff system of ordinary differential equations, making use of $n$ starting values. The method is exact if the problem is of the form $y’(t) = Py(t) + Q(t)$, where $P$ is a constant and $Q(t)$ is a polynomial of degree $2n$.