Boundary-value technique for the numerical solution of periodic parabolic problems

1978 ◽  
pp. 41-55 ◽  
Author(s):  
H. Koßmann
Keyword(s):  
Numerical Solution ◽  
Boundary Value ◽  
Parabolic Problems

scholarly journals Splitting least squares and collocation procedures for two-point boundary value problems

1985 ◽  
Vol 27 (2) ◽  
pp. 167-193
Author(s):  
John Locker ◽  
P. M. Prenter
Keyword(s):  
Linear System ◽  
Boundary Value Problem ◽  
Numerical Solution ◽  
Least Squares ◽  
Boundary Value ◽  
Linear Operators ◽  
Point Boundary ◽  
System Error ◽  
Densely Defined ◽  
Split System

AbstractLet L, T, S, and R be closed densely defined linear operators from a Hubert space X into X where L can be factored as L = TS + R. The equation Lu = f is equivalent to the linear system Tv + Ru = f and Su = v. If Lu = f is a two-point boundary value problem, numerical solution of the split system admits cruder approximations than the unsplit equations. This paper develops the theory of such splittings together with the theory of the Methods of Least Squares and of Collocation for the split system. Error estimates in both L2 and L∞ norms are obtained for both methods.

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