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Dynamical modeling, General ODE - Coggle Diagram

- - - - First
      - Second
        
        Elliptic
        
        Parabolic
        
        Hyperbolic
      - Third
    - - Linear
      - Quasi-linear
      - Non-linear
    - - Dirichlet conditions
      - Neumann conditions
      - Robbins conditions
- - - - Adventages
        
        Easy
        
        Visualization method
      - Disadaventages
        
        Take a long time and may be not suitable in very complex problem with high specificity solution requires
    - - Advantages
        
        Faster
        
        Use only one of initial value
        
        Based on Taylor series
      - Disadvantages
        
        Division by zero problem can occur.
        
        Must calculate derivative
    - - Advantages
        
        Simple and direct
        
        enable for non linear
      - Disadvantages
        
        Less accuracy
        
        Truncation error
    - - 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.

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Dynamical modeling

Disadaventages

General ODE

Classification

Order

Linearity

Homogeneity

Boundary

Canonical form

alternative form, Common form, STD form

General solution by MATLAB

Use function >>dslove()

ODE

Solution by numerical methods

Graphical method

Adventages

Disadaventages

Take a long time and may be not suitable in very complex problem with high specificity solution requires

Easy

Visualization method

Newton-raphson

Advantages

Disadvantages

Faster

Use only one of initial value

Based on Taylor series

Division by zero problem can occur.

Must calculate derivative

Euler method

Advantages

Disadvantages

Simple and direct

enable for non linear

Less accuracy

Truncation error

click to edit

Runge-Kutta

Advantages

Use Taylor series

Disadvantages

Take a very long time

Difficult for error estimation

Stable

Easy to implement

Not good for systems of differential equations with a mix of fast and slow state dynamics.

PDE

Multiple variables

Classification

Order

First

Second

Third

Dynamical process

Linearity

Linear

Quasi-linear

Non-linear

Boundary condition

Dirichlet conditions

Neumann conditions

Robbins conditions

Elliptic

Parabolic

Hyperbolic