Método de Euler (1 passo)
- Created by
- Renato Passos, Eng. de Software
- Reviewed by
- Renato Passos, Eng. de Software
Last updated: Apr 18, 2026
Formula
Euler
About this calculator
The Euler Method (1 step) calculator numerically solves first-order ordinary differential equations (ODEs) by approximating the solution step by step. It uses the formula y_{n+1} = y_n + h · f(x_n, y_n), where h is the step size. The user inputs the ODE as y' = f(x, y), the initial condition (x0, y0), and the step h, and the calculator generates a sequence of approximate points.
This method is simple and fast, ideal for obtaining an initial estimate of an ODE solution. It is widely used in engineering, physics, and biology problems, such as radioactive decay, population growth, or electrical circuits. As a first-order method, the accumulated error is proportional to h, requiring small steps for better accuracy.
Cautions: the method can be unstable for large steps or stiff equations. Always check if the ODE is well-behaved and consider more accurate methods (like Runge-Kutta) for reliable results. The calculator provides only approximations; it does not replace analytical solutions when available.
Frequently asked questions
What is the difference between Euler's Method and Runge-Kutta Method?
Euler's Method is a first-order method, simple with error proportional to step h. Runge-Kutta (e.g., RK4) is fourth-order, more accurate and stable, but requires more calculations per step.
How do I choose the step size h?
Use a small enough h so that the solution does not oscillate or blow up. For simple equations, h between 0.1 and 0.01 usually works. Test by reducing h and see if results change little.
Does the method work for any ODE?
It works for well-behaved first-order ODEs. For stiff equations or discontinuities, the method may fail. In such cases, use implicit or adaptive methods.
Why is my result diverging?
Divergence may occur if the step h is too large, the ODE is unstable, or the initial condition is incorrect. Try reducing h or check the ODE.
Can I use the method for systems of ODEs?
Yes, Euler's Method can be extended to systems of ODEs by applying the formula to each equation simultaneously. This calculator, however, solves only a single first-order ODE.