Compact difference scheme for parabolic and Schrödinger-type equations with variable coefficients

Vladimir Gordin; Evgenii Tsymbalov

doi:10.1016/j.jcp.2018.06.079

paper

Compact difference scheme for parabolic and Schrödinger-type equations with variable coefficients

arXiv:1712.05214 · doi:10.1016/j.jcp.2018.06.079

Abstract

We develop a new compact scheme for second-order PDE (parabolic and Schrödinger type) with a variable time-independent coefficient. It has a higher order and smaller error than classic implicit scheme. The Dirichlet and Neumann boundary problems are considered. The relative finite-difference operator is almost self-adjoint.

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