Stability of sequences generated by nonlinear differential systems

Author:
R. Leonard Brown

Journal:
Math. Comp. **33** (1979), 637-645

MSC:
Primary 65L99; Secondary 34D20

DOI:
https://doi.org/10.1090/S0025-5718-1979-0521279-9

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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Additional Information

DOI:
https://doi.org/10.1090/S0025-5718-1979-0521279-9

Keywords:
Initial value problem,
numerical integration of ordinary differential equations,
discrete Liapunov function,
stability of nonlinear sequences

Article copyright:
© Copyright 1979
American Mathematical Society