Orthogonal Spline Collocation Methods for Schrr Odinger-type Equations in One Space Variable
نویسندگان
چکیده
We examine the use of orthogonal spline collocation for the semi-discretization of the cubic Schrr odinger equation and the two-dimensional parabolic equation of Tappert. In each case, an optimal order L 2 estimate of the error in the semidiscrete approximation is derived. For the cubic Schrr odinger equation, we present the results of numerical experiments in which the integration in time is performed using a routine from a software library.
منابع مشابه
Osc Methods for Schr Odinger Equation
Two discrete-time orthogonal spline collocation schemes are formulated and analyzed for solving the linear time-dependent Schrr odinger equation in two space variables. These are Crank-Nicolson and alternating direction implicit (ADI) schemes employing C 1 piecewise polynomial spaces of arbitrary degree 3 in each space variable. The stability of the schemes is examined and optimal order a prior...
متن کاملOdinger-type Equations in One Space Variable
We examine the use of orthogonal spline collocation for the semi-discretization of the cubic Schr odinger equation and the two-dimensional parabolic equation of Tappert. In each case, an optimal order L 2 estimate of the error in the semidiscrete approximation is derived. For the cubic Schr odinger equation, we present the results of numerical experiments in which the integration in time is p...
متن کاملInstitute for Mathematical Physics on Separation of Variables in the Schrr Odinger Equation for a Particle Interacting with External Field on Separation of Variables in the Schrr Odinger Equation for a Particle Interacting with External Eld
We obtain the most general form of the vector-potential of the electromagnetic eld A enabling separation of variables in the (1+2)-dimensional Schrr odinger equation (SE). Using this result we have carried out variable separation for a class of Schrr odinger equations that contains as particular cases SE with Coulomb scalar potential and SE for a particle interacting with the constant magnetic ...
متن کاملA spline collocation method for integrating a class of chemical reactor equations
. In this paper, we develop a quadratic spline collocation method for integrating the nonlinear partial differential equations (PDEs) of a plug flow reactor model. The method is proposed in order to be used for the operation of control design and/or numerical simulations. We first present the Crank-Nicolson method to temporally discretize the state variable. Then, we develop and analyze the pro...
متن کاملA Third-degree B-spline Collocation Scheme for Solving a Class of the Nonlinear Lane–-Emden Type Equations
In this paper, we use a numerical method involving collocation method with third B-splines as basis functions for solving a class of singular initial value problems (IVPs) of Lane--Emden type equation. The original differential equation is modified at the point of singularity. The modified problem is then treated by using B-spline approximation. In the case of non-linear problems, we first line...
متن کامل