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Mathematical Models and Computer Simulations

, Volume 10, Issue 1, pp 79–88 | Cite as

A Fourth-Order Accurate Difference Scheme for a Differential Equation with Variable Coefficients

  • V. A. GordinEmail author
  • E. A. Tsymbalov
Article

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.

Keywords

compact difference scheme divergent scheme test functions self-conjugacy 

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Copyright information

© Pleiades Publishing, Ltd. 2018

Authors and Affiliations

  1. 1.Higher School of EconomicsNational Research UniversityMoscowRussia
  2. 2.Hydrometeorological Center of RussiaMoscowRussia
  3. 3.Skolkovo Institute of Science and TechnologyMoscowRussia

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