Summary
It is shown that Liapunov functions may be used to obtain error bounds for approximate solutions of systems of ordinary differential equations. These error bounds may reflect the behaviour of the error more accurately than other bounds.
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References
Cooper, G.J.: Error bounds for numerical solutions of ordinary differential equations. Numer. Math.18, 162–170 (1971)
Dahlquist, G.: Stability and error bounds in the numerical integration of ordinary differential equations. Trans. Royal Inst. Technology, Stockholm, 130, 1959
Hahn, W.: Stability of motion. Berlin-Heidelberg-New York: Springer 1967
Walter, W.: Differential and integral inequalities. Berlin-Heidelberg-New York: Springer 1970
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Cooper, G.J., Whitworth, F.C.P. Liapunov functions and error bounds for approximate solutions of ordinary differential equations. Numer. Math. 30, 411–414 (1978). https://doi.org/10.1007/BF01398508
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DOI: https://doi.org/10.1007/BF01398508