Euler Method Calculator
Apply forward Euler to y′ = f(x,y) with an initial condition, step size and target x. The calculator plots the numerical solution, reports endpoint error when an exact solution is supplied and exposes every computed point.
Expression syntax: use explicit multiplication such as 2*y. Supported functions include sin, cos, tan, exp, ln, sqrt and abs.
How this tool works
Forward Euler uses yₙ₊₁ = yₙ + h f(xₙ,yₙ) and xₙ₊₁ = xₙ + h. Its global truncation error is first order in h under standard smoothness assumptions.
Example
For y′ = −2y, y(0)=1 and h=0.1, Euler repeatedly follows the slope at the beginning of each interval. Compare the final value with exp(−2x).
Common questions
Why use Euler’s method if RK4 is more accurate?
Euler is simple, transparent and useful for learning consistency, truncation error and stability. It is also a convenient baseline for method comparisons.
Why can Euler become unstable?
Explicit Euler has a limited stability region. For rapidly decaying or stiff equations, a step size that is too large can make the numerical sequence oscillate or grow even when the true solution decays.