Difference schemes for second-order ordinary differential equations with corrector and predictor properties
-
Vladimir V. Shaidurov
and
Anton E. Novikov
Abstract
A technique for constructing a sequence of difference schemes with the properties of a corrector and a predictor for integrating systems of the second-order ordinary differential equations is presented. The sequence of schemes begins with the explicit three-point Störmer method of the second order of approximation. Each subsequent scheme also implements the Störmer method corrected with additional terms calculated through the solution of the previous scheme. The stability of the resulting schemes and the increase in the order of convergence for the first of them are carefully substantiated. The results of calculations of the test problem are presented, confirming the increase in the order of accuracy of the constructed methods.
Funding statement: This work was supported by the Krasnoyarsk Mathematical Center and financed by the Ministry of Science and Higher Education of the Russian Federation in the framework of the establishment and development of regional Centers for Mathematics Research and Education (Agreement No. 075-02-2021-1384).
Acknowledgment
The authors thank R. A. Golubev for prompt computational experiments.
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Articles in the same Issue
- Frontmatter
- Variational data assimilation for a sea dynamics model
- Connection between the existence of a priori estimate for a flux and the convergence of iterative methods for diffusion equation with highly varying coefficients
- Mesh scheme for a phase transition problem with time-fractional derivative
- A finite element scheme for the numerical solution of the Navier–Stokes/Biot coupled problem
- Difference schemes for second-order ordinary differential equations with corrector and predictor properties
Articles in the same Issue
- Frontmatter
- Variational data assimilation for a sea dynamics model
- Connection between the existence of a priori estimate for a flux and the convergence of iterative methods for diffusion equation with highly varying coefficients
- Mesh scheme for a phase transition problem with time-fractional derivative
- A finite element scheme for the numerical solution of the Navier–Stokes/Biot coupled problem
- Difference schemes for second-order ordinary differential equations with corrector and predictor properties
