So far, Fourth Order Runge-Kutta is the most popular and widely used. For many practical purposes, you may use this solution.
Suppose we have ODE then
Error term : , correct up to the third order term in Taylor series expansion
, set , with initial condition . The few first results and the graph of solution are given below.
Note that after , the solution is not correct. See Comparison .
Preferable reference for this tutorial is
Teknomo, Kardi (2015) Solving Ordinary Differential Equation (ODE). https:\\people.revoledu.com\kardi\tutorial\ODE\