PHYS 305: Computational Physics II

Winter 2014

The Simple Harmonic Oscillator Revisited

The Simple Harmonic Oscillator serves as a standard model in Mechanics and Quantum Mechanics. Yet it is very easy to understand and, therefore, very useful.

Here we propose to use SHO as a standard for coding the numerical approaches to solve ODEs, Euler, Mid-Point and rk4.

The following provides complete C codes that solve the SHO over an arbitrary time interval spanned by an arbitrary time grid, using default potential parameter and mass. These codes illustrate diverse coding styles.

Euler Method
- Simplest code: HO_euler.c
- Using struct to store parameters: HO_struct.c
- Using function pointers: HO_pointer.c
- Using struct and function pointers : HO_struct_pointer.c
Mid-point

Using struct to store parameters: HO_mid_point_struct.c

Runge-Kutta 4th order

Using struct to store parameters: HO_rk4_struct.c

Time stepper

Simplest - no struct: euler_step.c, mid_point_step.c, rk4_step.c,
Using a struct: Euler_step_struct.c, Mid_Point_step_struct.c, rk4_step_struct.c,

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