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Dynamical modeling, General ODE - Coggle Diagram
Dynamical modeling
PDE
Multiple variables
Classification
Order
First
Second
Elliptic
Parabolic
Hyperbolic
Third
Linearity
Linear
Quasi-linear
Non-linear
Boundary condition
Dirichlet conditions
Neumann conditions
Robbins conditions
Dynamical process
ODE
Solution by numerical methods
Graphical method
Adventages
Easy
Visualization method
Disadaventages
Take a long time and may be not suitable in very complex problem with high specificity solution requires
Newton-raphson
Advantages
Faster
Use only one of initial value
Based on Taylor series
Disadvantages
Division by zero problem can occur.
Must calculate derivative
Euler method
Advantages
Simple and direct
enable for non linear
Disadvantages
Less accuracy
Truncation error
Runge-Kutta
Advantages
Use Taylor series
Stable
Easy to implement
Disadvantages
Take a very long time
Difficult for error estimation
Not good for systems of differential equations with a mix of fast and slow state dynamics.
General ODE
Classification
Order
Linearity
Homogeneity
Boundary
Canonical form
alternative form, Common form, STD form
General solution by MATLAB
Use function >>dslove()