Paper Info
Title
An Alternating-Direction Implicit Orthogonal Spline Collocation Scheme for Nonlinear Parabolic Problems on Rectangular Polygons
Abstract
We consider a nonlinear parabolic initial-boundary value problem on a rectangular polygon with the solution satisfying Robin boundary conditions with variable coefficients. An approximation to the solution at the desired time value is obtained using an alternating-direction implicit extrapolated Crank--Nicolson scheme in which orthogonal spline collocation with piecewise polynomials of an arbitrary degree is used for spatial discretization. At each time level, the scheme determines the intermediate solution along horizontal lines and the approximate solution along vertical lines passing through the Gauss points. Only at the last time level is the approximate solution along vertical lines converted into the approximate solution defined on the entire rectangular polygon. This property of our approach leads to its efficient implementation and its applicability to rectangular polygons.
Year
DOI
Venue
2006
10.1137/050627885
SIAM J. Scientific Computing
Keywords
Field
DocType
nicolson scheme,rectangular polygon,time value,rectangular polygons,entire rectangular polygon,approximate solution,time level,last time level,alternating-direction implicit orthogonal spline,intermediate solution,nonlinear parabolic initial-boundary value,vertical line,nonlinear parabolic problems,collocation scheme,extrapolation,implementation,alternating direction implicit
Alternating direction implicit method,Boundary value problem,Discretization,Polygon,Mathematical optimization,Robin boundary condition,Mathematical analysis,Initial value problem,Mathematics,Piecewise,Parabola
Journal
Volume
Issue
ISSN
28
3
1064-8275
Citations 
PageRank 
References 
8
1.66
3
Authors
2
Name
Order
Citations
PageRank
Bernard Bialecki111418.61
Ryan I. Fernandes2345.16