scholarly journals Accuracy of the numerical solution of a two-point boundary value problem by the orthogonal collocation method.

1995 ◽  
Vol 28 (3) ◽  
pp. 316-323 ◽  
Author(s):  
Fumihide Shiraishi ◽  
Takahiro Hasegawa ◽  
Hiroyuki Nagasue
Keyword(s):  
Boundary Value Problem ◽  
Numerical Solution ◽  
Collocation Method ◽  
Boundary Value ◽  
Point Boundary ◽  
Orthogonal Collocation

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.

scholarly journals A Barycentric Interpolation Collocation Method for Linear Nonlocal Boundary Value Problems

2016 ◽  
Vol 10 (11) ◽  
pp. 140
Author(s):  
Dan Tian ◽  
Weiya Li ◽  
Cec Yulan Wang
Keyword(s):  
Boundary Value Problem ◽  
Collocation Method ◽  
Present Method ◽  
Lagrange Interpolation ◽  
Boundary Value ◽  
Nonlocal Boundary ◽  
Higher Order ◽  
Point Boundary ◽  
Numerical Treatment ◽  
Barycentric Interpolation

This paper is devoted to the numerical treatment of a class of higher-order multi-point boundary value problem-s(BVPs). The method is proposed based on the Lagrange interpolation collocation method, but it avoids thenumerical instability of Lagrange interpolation. Numerical results obtained by present method compare with othermethods show that the present method is simple and accurate for higher-order multi-point BVPs, and it is eectivefor solving six order or higher order multi-point BVPs.

A multipoint Birkhoff type boundary value problem

2015 ◽  
Vol 23 (1) ◽  
pp. 1-11 ◽  
Author(s):  
Francesco A. Costabile ◽  
Anna Napoli
Keyword(s):  
Boundary Value Problem ◽  
Numerical Solution ◽  
Collocation Method ◽  
Existence And Uniqueness ◽  
Boundary Value ◽  
Uniqueness Of Solution ◽  
Multipoint Boundary ◽  
Type Boundary ◽  
Theoretical Results ◽  
Multipoint Boundary Value Problem

AbstractA multipoint boundary value problem is considered. The existence and uniqueness of solution is proved. Then, for the numerical solution, a general collocation method is proposed.Numerical experiments confirm theoretical results.

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