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

We develop a new compact scheme for the 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 ope...

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Veröffentlicht in:	Journal of computational physics 2018-12, Vol.375, p.1451-1468
Hauptverfasser:	Gordin, Vladimir A., Tsymbalov, Evgenii A.
Format:	Artikel
Sprache:	eng
Schlagworte:	Compact difference scheme Computational physics Dirichlet problem Finite difference method Finite differences Implicit scheme Matrix Neumann boundary conditions Operators (mathematics) Parabolic equation Partial differential equations Self-adjointness Test functions
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