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- Title
Dependence of the Analytical Approximate Solution to the Van der Pol Equation on the Perturbation of a Moving Singular Point in the Complex Domain.
- Authors
Orlov, Victor
- Abstract
This paper considers a theoretical substantiation of the influence of a perturbation of a moving singular point on the analytical approximate solution to the Van der Pol equation obtained earlier by the author. A priori estimates of the error of the analytical approximate solution are obtained, which allows the solving of the inverse problem of the theory of error: what should the structure of the analytical approximate solution be in order to obtain a result with a given accuracy? Thanks to a new approach for obtaining a priori evaluations of errors, based on elements of differential calculus, the domain, used to obtain an analytical approximate solution, was substantially expanded. A variant of optimizing a priori estimates using a posteriori estimates is illustrated. The results of a numerical experiment are also presented.
- Subjects
SINGULAR perturbations; PERTURBATION theory; ERROR analysis in mathematics; INVERSE problems; DIFFERENTIAL calculus
- Publication
Axioms (2075-1680), 2023, Vol 12, Issue 5, p465
- ISSN
2075-1680
- Publication type
Article
- DOI
10.3390/axioms12050465