4. Ordinary Differential Equations (ODE)

Find the solution of

( etc.)

In physics:

- mostly first or second order

- usually given in explicit form, or

Second order DE may be written as 2 DEs of first order: ; .

Harmonic oscillator: Instead of , write

or

- If the values of , etc. are all given at :

- If , etc. are given at several points
:

*Boundary Value Problem* (BVP).

Typical IVP: *equations of motion*
;
and given

Typical BVP: potential equation
;
given at boundary points

- 4.1 Initial Value Problems of First Order
- 4.1.1 Euler-Cauchy Algorithm
- 4.1.2 Stability and Accuracy of Difference Schemes
- 4.1.3 Explicit Methods
- 4.1.4 Implicit Methods
- 4.1.5 Predictor-Corrector Method
- 4.1.6 Runge-Kutta Method

- 4.2 Initial Value Problems of Second Order
- 4.2.1 Verlet Method
- 4.2.2 Predictor-Corrector Method for 2nd order ODE
- 4.2.3 Nordsieck Formulation of the PC Method
- 4.2.4 Runge-Kutta Method for 2nd order ODE
- 4.2.5 Symplectic Algorithms
- 4.2.6 Numerov's Method

- 4.3 Boundary Value Problems

See also: