A computational study of the discretization error in the solution of the Spencer-Lewis equation by doubling applied to the upwind finite- difference approximation. (English) Zbl 0767.65092
This paper is a comprehensive study of the discretization error associated with the upwind finite difference method when applied to a model solution of the Spencer-Lewis equation. This model leads to a system of 2 differential equations for \(u\) and \(v\) which are the angular fluxes of right moving and left moving electrons respectively. The derivatives are in terms of the one-dimensional co-ordinate \(z\) and the electron energy \(E\). A set of conditions is deduced from this study, for the reduction of the error.
Reviewer: B.Burrows (Stafford)
MSC:
| 65Z05 | Applications to the sciences |
| 65N06 | Finite difference methods for boundary value problems involving PDEs |
| 78A35 | Motion of charged particles |
| 35Q60 | PDEs in connection with optics and electromagnetic theory |
| 35Q40 | PDEs in connection with quantum mechanics |
| 81V10 | Electromagnetic interaction; quantum electrodynamics |
Keywords:
electron transport; charged-particle transport; discretization error; upwind finite difference method; Spencer-Lewis equation; moving electronsReferences:
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