What are the methods for solving ODEs with accuracy higher than Runge Kutta 4?

Question

Usually, justification of using RK4 is the following: "RK4 demonstrates a better approximations than Euler and Modified Euler methods of solving ODEs and offers a good balance between accuracy and computation cost".

What are the other methods of solving ODEs that are more computationally expensive but offer a higher accuracy?

Answer 1

You can check for instance DifferentialEquations.jl which has many relevant solvers implemented.