Numerical methods: principles, analyses, and algorithms

Abstract

1. Background to Numerical Methods 2. Scope of Mathematical and Numerical Methods 3. Errors and their Propagation 4. Programming Tools and Techniques 5. Numerical Solution of One-Dimensional Non-Linear Equations 6. Numerical Solution of Linear Equations: Direct Methods 7. Numerical Solutions for Matrix Inversion 8. Numerical SOlution of Linear Systems of Equations: Iterative Methods 9. Eigenvalues and Eigenvalues 10. Numerical Solution of Systems of Nonlinear Equations 11. Linear Least Squares Problem 12. Interpolation and Extrapolation 13. Numerical Differentiation 14. Numeical Integration 15. Numerical Solution of Ordinary Differential Equations: Initial Value Problem 16. Numerical Solution of Ordinary Differential Equations: Boundary value Problem 17. Partial Differential Equations 18. Numerical Solution of Parabolic Partial Differential Equations 19. Numerical Solution of Hyperbolic Partial Differential Equations 20. Numerical Solution of Elliptic Partial Differential Equations 22. Advances in Numerical Methods Using Neurocomputing Paradigm 23. Numerical Solution of Differential Equations