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The INITIAL VALUE PROBLEM
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Contents
ORDINARY DIFFERENTIAL EQUATIONS
Subsections
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)
Convergence Analysis for ERK
Multi-step Methods
Backward Differentiation Formulas (BDF's)
Stability and Stiff Equations
The Linear Stability domain and A-Stability
-Stability of Runge-Kutta
A-Stability of Multistep Methods
Linear Stability of Adams-Bashforth and Adams-Moulton Schemes
BOUNDARY VALUE PROBLEMS (BVP)
The Shooting Method
The Shooting Method, Nonlinear Case
Finite Difference Technique
The Method of Weighted Residuals (MWR)
Subdomain Method
Collocation Method:
Galerkin Method:
Variational Formulation
Variational formulation for a second-order linear ODE
The Finite Element Method FEM
Juan Restrepo 2003-05-02
-Stability of Runge-Kutta