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Mathematics of Computation

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Stability of sequences generated by nonlinear differential systems

Author: R. Leonard Brown
Journal: Math. Comp. 33 (1979), 637-645
MSC: Primary 65L99; Secondary 34D20
MathSciNet review: 521279
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Abstract: A local stability analysis is given for both the analytic and numerical solutions of the initial value problem for a system of ordinary differential equations. The standard linear stability analysis is reviewed, then it is shown that, using a proper choice of Liapunov function, a connected region of stable initial values of both the analytic solution and of the one-leg k-step numerical solution can be approximated computationally. Correspondence between the one-leg k-step solution and its associated linear k-step solution is shown, and two examples are given.

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Keywords: Initial value problem, numerical integration of ordinary differential equations, discrete Liapunov function, stability of nonlinear sequences
Article copyright: © Copyright 1979 American Mathematical Society

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