Abstract
Through a detailed analysis of the properties of a system of differential equations, bounds are given for the error affecting the final result of a numerical integration. These bounds appear to be narrower than those obtained with other methods. The key procedure is to consider carefully the linear part of the system and to bound it taking account of all possible errors. No very significant restriction is made on the system.
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References
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This work was partially supported by the Ministero della Pubblica Istruzione.
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De Gregorio, S. Narrow bounds for numerical integration of differential equations. J Stat Phys 41, 865–876 (1985). https://doi.org/10.1007/BF01010007
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DOI: https://doi.org/10.1007/BF01010007