06_ODE_Solvers

The OSP library includes multiple integrators for ordinary differential equations. Each solver implements the interface:

public interface ODESolver {
   void initialize(double stepSize);
   void setStepSize(double stepSize);
   double getStepSize();
   void step();
   // ...
}

and works with and ODE instance:

public interface ODE {
   double[] getState();
   void getRate(double[] state, double[] rate);
}

Common Solvers

1. Euler
   • Simple, first-order.
   • new Euler(myODE)
2. EulerRichardson (also known as the “midpoint method”)
   • Second-order. Good for many typical physics problems.
3. RK4 (Runge-Kutta 4)
   • Fourth-order method; a good general-purpose solver.
4. RK45
   • Adaptive step-size method (Dormand-Prince) with error estimation.
5. Verlet / VelocityVerlet
   • Often used in molecular dynamics, preserves better energy behavior in certain Hamiltonian systems.

Example Usage

ODE myODE = new FallingParticleODE(); 
ODESolver solver = new Euler(myODE);
solver.setStepSize(0.01);
while(myODE.getState()[0]>0){ // e.g. while y>0
   solver.step();
}

See the OSP manual or the “CSM” examples for more advanced usage (e.g., event handling, collisions, etc.).