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Contents
Contents
Contents
ORDINARY DIFFERENTIAL EQUATIONS
The INITIAL VALUE PROBLEM (IVP)
Some important theorems on ODE's
Numerical Methods for the approximate solution of ODE'S.
Generalizations of Forward Euler by its Different Interpretations
Errors in the Numerical Approximation of the IVP
How is the Approximation Related to the IVP, if at all?
Taylor-series Method
Trapezoidal Rule
Theta Method
The Runge-Kutta Family (RK)
Multi-step Methods
Backward Differentiation Formulas (BDF's)
Stability and Stiff Equations
BOUNDARY VALUE PROBLEMS (BVP)
The Method of Weighted Residuals (MWR)
Subdomain Method
Collocation Method:
Galerkin Method:
Variational Formulation
The Finite Element Method FEM
PARTIAL DIFFERENTIAL EQUATIONS (PDE's)
INTRODUCTION
Basic Methods for Numerical Approximation of PDE
HYPERBOLIC EQUATIONS
PARABOLIC EQUATIONS AND THE ADVECTION-DIFFUSION EQUATION
Properties of the Solution
Finite Difference Schemes
Reduction of Parabolic Equations to a System of ODE's
HIGHER-ORDER EVOLUTION EQUATIONS AND SPLIT-STEP METHODS
ELLIPTIC EQUATIONS
NUMERICAL METHODS FOR THE SOLUTION OF THE POISSON EQUATION
Fundamentals of Multigrids Methods
APPENDIX
Computing a Matrix Exponential
About this document ...
Juan Restrepo 2003-05-02
