Abstract
A new technique for the construction of numerical methods based on continued fractions is proposed. A characteristic feature of these algorithms is the fact that for certain values of the parameters it is possible to obtain both novel and traditional (explicit and implicit) numerical methods for the solution of the Cauchy problem for ordinary differential equations. Two-sided formulas are proposed by means of which it is possible to obtain on each integration step not only upper and lower approximations to the exact solution, but also information concerning the magnitude of the leading term of the error without the need for additional calculations of the right-hand side of the initial differential equation.
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Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 44, No. 12, pp. 1695–1701, December, 1992.
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Pelekh, Y.M. An approach to deducing approximate solutions to the Cauchy problem for nonlinear differential equations. Ukr Math J 44, 1554–1560 (1992). https://doi.org/10.1007/BF01061280
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DOI: https://doi.org/10.1007/BF01061280