Email this article A Fourth-Order Accurate Difference Scheme for a Differential Equation with Variable Coefficients
- Authors: Gordin V.A.1,2, Tsymbalov E.A.1,3
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Affiliations:
- Higher School of Economics
- Hydrometeorological Center of Russia
- Skolkovo Institute of Science and Technology
- Issue: Vol 10, No 1 (2018)
- Pages: 79-88
- Section: Article
- URL: https://journals.rcsi.science/2070-0482/article/view/202088
- DOI: https://doi.org/10.1134/S2070048218010064
- ID: 202088
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Abstract
A compact difference scheme on a three-point stencil for an unknown function is proposed. The scheme approximates a second-order linear differential equation with a variable smooth coefficient. Our numerical experiment confirms the fourth order of accuracy of the solution of the difference scheme and of the approximation of the eigenvalues of the boundary problem. The difference operator is almost self-adjoint and its spectrum is real. Richardson extrapolation helps to increase the order of accuracy.
About the authors
V. A. Gordin
Higher School of Economics; Hydrometeorological Center of Russia
Author for correspondence.
Email: vagordin@mail.ru
Russian Federation, Moscow; Moscow
E. A. Tsymbalov
Higher School of Economics; Skolkovo Institute of Science and Technology
Email: vagordin@mail.ru
Russian Federation, Moscow; Moscow
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