Runge–Kutta Solver for Systems: Step-by-Step Solutions

Euler and RK4 for two coupled equations (and second-order equations). Every step of the solution is shown, as you would write it on paper, using exact fractions.

What it solves

Euler or RK4 for two coupled equations. A second-order equation $x^{\prime \prime }=F(t,x,x^{\prime })$ becomes a system with $y=x^{\prime }$: $x^{\prime }=y$, $y^{\prime }=F(t,x,y)$.

How to use it

1. Enter your own numbers or functions in the boxes (an example is already filled in, or press Random example).
2. Check the equation preview, then press Solve step by step.
3. Reveal the solution one step at a time with Next step, or show everything at once.

Need the theory first? Read Section 8.8: Numerical Methods V: Higher-Order Equations and Systems, which explains the method in small steps with worked examples and exercises, then come back and test yourself with the Chapter 8 quiz.

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