Compact difference scheme for parabolic and Schrödinger-type equations with variable coefficients
arXiv:1712.0521412 citationsh-index: 11
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Provides a more accurate numerical method for solving PDEs with variable coefficients, benefiting computational scientists working on time-dependent problems.
Developed a compact finite-difference scheme for parabolic and Schrödinger-type equations with variable coefficients, achieving higher order and smaller error than classic implicit schemes.
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.