Contents

•  Introduction

 
• Part I Theoretical Foundation
1 Self-adjoint operator
2 Dirac delta function
3 Construction of Green's function
3.1 One Dimension
3.2 Two Dimensions
4 Fourier Series for boundary value problem
5 Asymptotic Error Expansion
• Part II Numerical Experiments
1 One-dimensional Problems
1.1 Forcing Function 
1.2 Forcing Function 
1.3 Forcing Function 
1.4 Forcing Function
1.5 Forcing Function
2 Two-dimensional Problems
2.1 Forcing Function
2.2 Forcing Function
2.3 Forcing Function
• Conculsion
• References
• Appendix A
Experiment 1a
Experiment 1b
Experiment 1c
• Appendix B
Experiment 2a
Experiment 2b
Experiment 2c
Experiment 2d
Experiment 2e
Experiment 2f
Experiment 2g
Experiment 2h
• Appendix C
Experiment 3a
Experiment 3b
Experiment 3c
Experiment 3d
Experiment 3e
Experiment 3f
Experiment 3g
Experiment 3h
• Appendix D
Experiment 4a
Experiment 4b
Experiment 4c
Experiment 4d
• Appendix E
Experiment 5a
Experiment 5b
Experiment 5c
Experiment 5d
• Appendix F
Experiment 6a
Experiment 6b
Experiment 6c
• Appendix G
Experiment 7a
Experiment 7b
Experiment 7c
Experiment 7d
Experiment 7e