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Mathematics of Computation

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

Author: R. K. Jain
Journal: Math. Comp. 26 (1972), 71-77
MSC: Primary 65L05
MathSciNet review: 0303733
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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 $2n$.

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Keywords: Stiff system of ordinary differential equations, <IMG WIDTH="21" HEIGHT="20" ALIGN="BOTTOM" BORDER="0" SRC="images/img1.gif" ALT="$A$">-stability, multi-step methods, Lagrangian interpolation polynomials, Hermite interpolation polynomials
Article copyright: © Copyright 1972 American Mathematical Society