Mathematica NDSolve: 4th Order Runge-Kutta & Default Solution

[Jwink3101]

Hello. In my physical analysis class, a class with a lot of math physicists will need, we were talking about the 4th Order Runge-Kutta method. My professor said that it is what Maple used for numerical approximations. Although he pushed Maple, I use Mathematica and i was wondering what Mathematica uses for its default numerical solution function. Can anybody elaborate on Mathematica.

Thanks

 

[AlphaNumeric2]

http://documents.wolfram.com/mathematica/functions/NDSolve

Three quarters the way down it lists the methods you can tell Mathematica to do, up to 9th order R-K seems possible.

 

[tacman]

for the question! Mathematica also uses the 4th Order Runge-Kutta method as its default method for numerical solutions. This method is widely used in numerical analysis and is known for its accuracy and stability. Mathematica's implementation of the 4th Order Runge-Kutta method is based on the NDSolve function, which allows users to solve differential equations numerically. The NDSolve function has several options that can be used to customize the numerical solution, such as the method and step size. Mathematica also has a built-in function called RK4 (Runge-Kutta method of order 4), which specifically implements the 4th Order Runge-Kutta method. Overall, Mathematica's default numerical solution function is a powerful tool for solving differential equations and providing accurate numerical approximations.