Geodesic
4$^{\mathrm{th}}$ order difference scheme for the differential equation with variable coefficients
Matematičeskoe modelirovanie, Tome 29 (2017) no. 7, pp. 3-14.

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We present compact difference scheme on three-point stencil for unknown function. The scheme approximates linear second order differential equation with variable smooth coefficient. Our numerical experiments confirmed 4-th accuracy order of solutions of the difference scheme and of eigenvalues’ approximation for the boundary problem. The difference operator is almost self-conjugate, and its spectrum is real. The Richardson extrapolation method improves the accuracy order.
Keywords: compact difference scheme, test functions, self-conjugacy.
Mots-clés : divergent scheme 
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V. A. Gordin; E. A. Tsymbalov. 4$^{\mathrm{th}}$ order difference scheme for the differential equation with variable coefficients. Matematičeskoe modelirovanie, Tome 29 (2017) no. 7, pp. 3-14. http://geodesic.mathdoc.fr/item/MM_2017_29_7_a0/

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