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In this paper, we propose a class of exact artificial boundary conditions for the numerical solution of the Schrödinger equation on unbounded domains in two-dimensional cases. After we introduce a circular artificial boundary, we get an initial-boundary problem on a disc enclosed by the artificial boundary which is equivalent to the original problem. Based(More)
A local time-splitting method (LTSM) is developed to design absorbing boundary conditions for numerical solutions of time-dependent nonlinear Schrödinger equations associated with open boundaries. These boundary conditions are significant for numerical simulations of propagations of nonlinear waves in physical applications, such as nonlinear fiber optics(More)
We propose an adaptive approach in picking the wave-number parameter of absorbing boundary conditions for Schrödinger-type equations. Based on the Gabor transform which captures local frequency information in the vicinity of artificial boundaries, the parameter is determined by an energy-weighted method and yields a quasi-optimal absorbing boundary(More)
In this paper, we propose a tailored-finite-point method for a type of linear singular perturbation problem in two dimensions. Our finite point method has been tailored to some particular properties of the problem. Therefore, our new method can achieve very high accuracy with very coarse mesh even for very small ε, i.e. the boundary layers and interior(More)
In this paper, the numerical solutions of the problems of heat equation in two dimensions on unbounded domains are considered. For a given problem, we introduce an artificial boundary F to finite the computational domain. On the artificial boundary F, we propose an exact boundary condition to reduce the given problem to an initial-boundary problem of heat(More)
A new economical mixed nite element is formulated for the Stokes equations, in which the two components of the velocity and the pressure are deened on diierent meshes. First order error estimates are obtained for both the velocity and the pressure. Furthermore, the well known MAC method is derived from the resulting nite element method and the optimal error(More)
We study the numerical solution of semilinear parabolic PDEs on unbounded spatial domains in R 2 whose solutions blow up in finite time. Of particular interest are the cases where = R 2 or is a sectorial domain in R 2. We derive the nonlinear absorbing boundary conditions for corresponding, suitably chosen computational domains and then employ a simple(More)