Publication Date
7-6-1972
Abstract
Let T be a positive constant, let D^n be the interior of the unit hypercube in R^n with boundary ∂D^n, let a(t;x1,x2,…,xn) be a strictly positive funtion, and consider the parabolic problem ut= ∇*a ∇u + s(t;x1,x2,…,xn) in D^nx[0,T]
Where
U(t)=0 on ∂D^nx[0,T]
And
U(0)=f
This report compares three A-stable marching procedures for approximating this problem by finite differences. The procedures considered are the pure explicit procedure (APX) with 6t sufficiently restricted to insure A-stability, the pure implicit procedure (PM) or backwards difference equation, and a recently developed pure implicit procedure (SOC) which is second order correct in time and space. The implementation of PM and SOC in D^n requires the solution of large linear systems at each time step, and fast Poisson solvers provide efficient techniques for solving similar systems. Thus we show that the Buneman Poisson solver can be “truncated” when it is applied to PM with a(t;x1,x2,…,xn)=costant.
Degree Name
Mathematics
Level of Degree
Doctoral
Department Name
Mathematics & Statistics
First Committee Member (Chair)
Alfred Samuel Carasso
Second Committee Member
Reuben Hersh
Third Committee Member
George Milton Wing
Language
English
Document Type
Dissertation
Recommended Citation
Buzbee, Billy Lewis. "Application Of Fast Poisson Solvers To The Numerical Approzimation Of Parabolic Problems.." (1972). https://digitalrepository.unm.edu/math_etds/222
