First-order linear ODE
Solve a constant-coefficient model.
Open calculatorMathematics / Free calculator
Euler & Runge–Kutta numerical solver
Solve a first-order initial value problem with Euler or classical fourth-order Runge–Kutta and inspect each iteration.
01 Your inputs
02 Your result
Enter your values and select Calculate.
The method
A worked example
For y′ = y, y(0) = 1, h = 0.1 and 10 steps, RK4 gives y(1) ≈ 2.7182797441. The independent exact solution is e ≈ 2.7182818285; absolute error is about 2.0843 × 10⁻⁶.
Assumptions & limits
Fixed-step Euler or RK4, 1–80 steps, nonzero positive or negative step size. Steps too small to distinguish intermediate x coordinates are rejected. This is not an adaptive or stiff solver. Repeat with a smaller step size to check convergence. Domain errors and nonfinite outputs are rejected. Expressions use a restricted parser; no JavaScript evaluation.
Calculation source: Selected expression parser and RK4 implementation from Math Workbench beta 0.5.