09-23-2018, 07:27 AM
I have been looking at various methods to numerically solve ODEs (Ordinary Differential Equations). Among the various methods you can find (in Wikipedia) a family of Runge-Kutta methods. The 4th order Runge-Kutta method is perhaps the most popular. It has been used by HP in various calculator Stat Pacs.
The family of various Runge-Kutta methods solve ODE of:
dy/dx = f(x,y)
One interesting "side effect" is that if:
dy/dx = f(x)
Then you can obtain methods for numerical integration. The 4th order Runge-Kutta method, in this case, becomes Simpson's rule. The interesting windfall here is using the various variants of Runge-Kutta as additional methods for numerical integration. These variant methods are basically a "free bonus" method for numerical integration, which you can explore and use in performing numerical integration.
Namir
The family of various Runge-Kutta methods solve ODE of:
dy/dx = f(x,y)
One interesting "side effect" is that if:
dy/dx = f(x)
Then you can obtain methods for numerical integration. The 4th order Runge-Kutta method, in this case, becomes Simpson's rule. The interesting windfall here is using the various variants of Runge-Kutta as additional methods for numerical integration. These variant methods are basically a "free bonus" method for numerical integration, which you can explore and use in performing numerical integration.
Namir