Solve first-order ODEs numerically. Compare Euler, Heun, and Runge-Kutta 4th Order (RK4) approximation methods side-by-side with CSV exports.
⚡ Interactive Calculation Engine Active
Please enable JavaScript in your browser to run live computations, 2D envelope diagrams, and export PDF reports.
How to Use Differential Equation Solver Online
Enter the derivative function expression dy/dx = f(x, y).
Specify the initial conditions (x0, y0) and the end x limit.
Set the step size parameter (h).
Select and compare approximation methods on the live line plot.
Numerical ODE Solvers
Initial Value Problems (IVPs) in physics and engineering represent dynamic rates of change. Numerical methods trace approximating step trajectories when analytic solutions are unavailable.
Frequently Asked Questions
What is the RK4 method?
Runge-Kutta 4th Order is a highly accurate numerical solver that evaluates four slopes per step to achieve 4th-order global error scaling.