What is Euler's method?
A numerical technique that advances an ODE solution using local slope estimates.
Euler's Method Calculator
Step forward from an initial condition using yₙ₊₁ = yₙ + h·f(xₙ, yₙ).
Set initial value problem
Choose the DE form, enter initial (x₀, y₀), step size h, and number of steps.
About this calculator
How to use Euler's Method Calculator, plus the formulas and logic behind the results.
Tool description
Euler's method is the simplest numerical solver for first-order ODEs, using the tangent slope at each step.
How to use
- Select ky or x+y as the right-hand side.
- Enter the initial condition, step size, and step count.
- Select Calculate to view the final estimate and table summary.
- Reduce h to improve accuracy (more steps for the same interval).
Formulas & reference
yₙ₊₁ = yₙ + h f(xₙ, yₙ)xₙ₊₁ = xₙ + h
Euler tips
- Exact solution of y′ = ky is y = y₀ e^{kx}
- Compare numeric y with the closed form when available
- h must be nonzero
- Too large h can drift far from the true solution
Calculation logic
Performs n forward Euler steps and reports the terminal (x, y) plus intermediate samples.
First-order accurate only—use small h for better approximations.
Euler's Method Calculator FAQ
Common questions about this calculator and how to use the results.
Which DEs are supported?
dy/dx = ky and dy/dx = x + y.
How do I choose h?
Smaller positive steps usually give better accuracy at the cost of more computation.
What is returned?
The approximate y after n steps and a short list of iterates.
Is it the same as Runge–Kutta?
No—Euler is the simplest special case; RK methods are higher order.
Can k be negative?
Yes—that models exponential decay.