Home | MATHS | Numerical Solution of Singular Eigenvalue

# Numerical Solution of Singular Eigenvalue

Added On :  03.06.2016 02:23 pm
For :  Numerical Methods

Numerical Solution of Singular Eigenvalue Problems for ODEs with a Focus on Problems Posed on Semi-Infinite Intervals - By R. Hammerling, O. Koch, Ch. Simon, and E. Weinm?ller.

Contents
1 Introduction 1
1.1 Mathematical Notation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Outline of the Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
2 Eigenvalue Problems for Ordinary Differential Equations 5
2.1 Sturm-Liouville Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
2.1.1 Example for a Sturm-Liouville Problem ? The Hydrogen Atom . . 8
2.2 Standard Codes for the Solution of Eigenvalue Problems in ODEs . . . . . 11
3 Problems Posed on Semi-Infinite Intervals 19
3.1 Transformation of the Independent Variable . . . . . . . . . . . . . . . . . 19
3.2 Implementation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
4 Collocation Methods for the Computation of Eigenvalues and Eigenfunctions 25
4.1 Conversion of the Eigenvalue Problem to a ?Standard? BVP . . . . . . . . 25
4.2 Singular Boundary Value Problems . . . . . . . . . . . . . . . . . . . . . . 26
4.3 Polynomial Collocation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
4.4 Convergence of Collocation Methods . . . . . . . . . . . . . . . . . . . . . 28
4.5 Numerical Example . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
4.6 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43
4.7 Implementation of the Eigenvalue Module . . . . . . . . . . . . . . . . . . 43
5 Matrix Methods 47
5.1 The Algebraic Eigenvalue Problem . . . . . . . . . . . . . . . . . . . . . . 47
5.2 A Matrix Method for a Singular First Order Differential EVP . . . . . . . 48
5.3 A Matrix Method for a Singular Second Order Differential EVP . . . . . . 54
5.4 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63
5.5 Matrix Method ? a Procedure for Obtaining Accurate Starting Profiles . . 63
5.6 Implementation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76
5.6.1 Files for this Module . . . . . . . . . . . . . . . . . . . . . . . . . . 76
5.6.2 Getting started . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76
5.6.3 Graphical User Interface Tutorial . . . . . . . . . . . . . . . . . . . 77
5.6.4 Graphical User Interface Controls . . . . . . . . . . . . . . . . . . . 78
5.6.5 The evpfile . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81
6 Conclusions 85

Tags : Book Numerical Solution of Singular Eigenvalue Pdf download Book Numerical Solution of Singular Eigenvalue by Pdf download Author written the book namely Numerical Solution of Singular Eigenvalue Author Pdf download Study material of Numerical Solution of Singular Eigenvalue Pdf download Lacture Notes of Numerical Solution of Singular Eigenvalue Pdf
Last 30 days 952 reviews