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

摘要

We develop a new compact scheme for the second-order PDE (parabolic and Schrodinger 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. (C) 2018 Elsevier Inc. All rights reserved.