Stability properties of some boundary value methods
Applied Numerical Mathematics
Stability of some boundary value methods for IVPs
NUMDIFF-7 Selected papers of the seventh conference on Numerical treatment of differential equations
High-order compact-difference schemes for time-dependent Maxwell equations
Journal of Computational Physics
Block-Boundary Value Methods for the Solution of Ordinary Differential Equations
SIAM Journal on Scientific Computing
Mathematics and Computers in Simulation
A semi-discrete higher order compact scheme for the unsteady two-dimensional Schrödinger equation
Journal of Computational and Applied Mathematics
Computers & Mathematics with Applications
Numerical solution of a biological population model using He's variational iteration method
Computers & Mathematics with Applications
Application of He's variational iteration method for solving the Cauchy reaction-diffusion problem
Journal of Computational and Applied Mathematics
Compact schemes for acoustics in the frequency domain
Mathematical and Computer Modelling: An International Journal
Applied Numerical Mathematics
Journal of Computational and Applied Mathematics
Computers & Mathematics with Applications
Journal of Computational Physics
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In this paper, a high-order and accurate method is proposed for solving the unsteady two-dimensional Schrodinger equation. We apply a compact finite difference approximation of fourth-order for discretizing spatial derivatives and a boundary value method of fourth-order for the time integration of the resulting linear system of ordinary differential equations. The proposed method has fourth-order accuracy in both space and time variables. Moreover this method is unconditionally stable due to the favorable stability property of boundary value methods. The results of numerical experiments are compared with analytical solutions and with those provided by other methods in the literature. These results show that the combination of a compact finite difference approximation of fourth-order and a fourth-order boundary value method gives an efficient algorithm for solving the two dimensional Schrodinger equation.