Forward Euler method
Also: Euler integration
A numerical update that projects the current slope across one time step.
x[k+1]=x[k]+Δt f(x[k],u[k]); accuracy and numerical stability depend on step size relative to dynamics.
- Formula
x[k+1] = x[k] + Δt f(x[k],u[k])
Example For dx/dt=−x/0.1 and Δt=0.02, x multiplies by 0.8.
Common misconception A stable continuous system can become numerically unstable with a coarse Euler step.