Numerical Methods for Partial Differential Equations · 2006 · 20 citations · 19 references
Natural SciencesMathematicsPhysicsComputational MechanicsComputational PhysicsDifferential EquationsApproximation MethodsBoundary ConditionsBoundary-value ProblemsNumerical AnalysisPartial Differential EquationsSchrödinger EquationArtificial Boundary ConditionsBoundary Condition ApproximationNumerical Analysis Of Partial Differential EquationsNumerical Methods For Initial Value ProblemsNumerical Solution Of The Schrödinger EquationNumerical Solutions Of Partial Differential EquationsPartial Differential Equation Solvers
Abstract We consider the numerical solution of the time‐dependent Schrödinger equation in ℝ 3 . An artificial boundary is introduced to obtain a bounded computational domain. On the given artificial boundary the exact boundary condition and a series of approximating boundary conditions are constructed, which are called artificial boundary conditions. By using the exact or approximating boundary conditions on the artificial boundary, the original problem is reduced to an equivalent or an approximate initial‐boundary value problem on the bounded computational domain. The uniqueness of the approximate problem is proved. The numerical results demonstrate that the method given in this article is effective and feasible. © 2006 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2007
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