Wolfram Library Archive

Courseware Demos MathSource Technical Notes
All Collections Articles Books Conference Proceedings

Mathematical Interpretation of the Boundary Conditions Phenomenon in the Refined Least Squares Method

Ryszard A. Walentynski
Organization: Silesia University of Technology, Poland
Department: Department of Building Structuresí Theory, Faculty of Civil Engineering

2003 International Mathematica Symposium
Conference location

Imperial College, London

The paper presents a mathematical explanation of the phenomenon observed for the Refined Least Squares method. It was found by numerical experiment with Mathematica that for some boundary-value or initial value problems it is possible to neglect selected boundary conditions and still obtain a nonsingular system of algebraic equations. Two examples present this phenomenon from the mathematical point of view and I make sense of the solution obtained. This discovery has an important application to ill-conditioned problems of mathematical physics and engineering. The approach makes it possible, in certain cases, to find an approximation which is valid on most of the domain, apart from the boundary layer, or to evaluate a main trend of the function.

*Mathematics > Calculus and Analysis > Differential Equations

Refined Least Squares method, boundary-value problems, initial value problems, nonsingular system of algebraic equations, boundary conditions phenomenon, refined least
Related items

*Challenging the Boundaries of Symbolic Computation: Proceedings of the 5th International Mathematica Symposium   [in Books]