Iterative solution of the nonlinear parabolic periodic boundary value problem

✍ Scribed by D.J. Evans; A. Benson

• Publisher: Elsevier Science
• Year: 1980
• Tongue: English
• Weight: 370 KB
• Volume: 22
• Category: Article
• ISSN: 0378-4754
• DOI: 10.1016/0378-4754(80)90005-1

✦ Synopsis

In this paper, the succcssi~c over-relaxation method IS.0.H.I is out2ined for the numerical soktion of the implicit finite difference equations deriued from the Crank-WicoZson approximation to a miZd2y non-2inear parabolic partial differsntia2 equation with periodic spatial. boundary conditions. The usual sepia2 ordering of the equations 71.5 shoun to be inconsistent, thus -&validating the we21 known S.O.R. theory of Young il.954), but a functional relationship between the eigcnvalues of the S.O.K. operator and the Jacobi operator of a c2osely ra2ated matrix is der?Cved, from which the optimum over-rehxation factor, oi, can 5~ determined directly. Nwn6riea2 experiments confirming the theorid developed arr giv& for tk chosen problem.