Methods for solving the initial value problem with a two-sided estimate of the local error

Fìz.-mat. model. ìnf. tehnol. 2021, 33:88-92

Abstract

Numerical methods for solving the initial value problem for ordinary differential equations are proposed. Embedded methods of order of accuracy 2(1), 3(2) and 4(3) are constructed. To estimate the local error, two-sided calculation formulas were used, which give estimates of the main terms of the error without additional calculations of the right-hand side of the differential equation, which favorably distinguishes them from traditional two-sided methods of the Runge- Kutta type.

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   DOI https://doi.org/10.1016/0041-5553(63)90023-5
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