Summary
Letu denote the approximation produced by a finite-difference method for solving an initial value problem for a given differential equation. Suppose the finite-difference equation is perturbed by a quantityw, e.g. due to round-off or truncation errors. Then, instead ofu, one obtains a solution which we denote byũ
In this paper a condition is presented which is necessary and sufficient for the existence of a two-sided estimate of the errorũ-u in terms of the perturbationw. The paper is concluded with applications in the fields of ordinary and partial parabolic differential equations.
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Spijker, M.N. On the possibility of two-sided error bounds in the numerical solution of initial value problems. Numer. Math. 26, 271–300 (1976). https://doi.org/10.1007/BF01395946
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DOI: https://doi.org/10.1007/BF01395946