A modified wide angle parabolic wave equation. (English) Zbl 0616.65093
We demonstrate the implicit finite difference discretization of a higher order parabolic-like partial differential equation approximating the reduced wave equation in the far field and show that the discretization is unconditionally stable. We discuss a method of associating an angle of dispersion with parabolic approximations, present an example which can be used to compare methods on the basis of dispersion angle, and make comparisons among well-known methods and the new method.
MSC:
| 65N12 | Stability and convergence of numerical methods for boundary value problems involving PDEs |
| 35K20 | Initial-boundary value problems for second-order parabolic equations |
| 81Q05 | Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics |
| 35J05 | Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation |
Keywords:
parabolic-like Schrödinger equation; pseudo-partial differential equation; unconditional stability; implicit finite difference discretization; reduced wave equation; dispersion; comparisonsReferences:
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