Stability Region Explorer: y' = λ y

Every step multiplies the solution by R(z) with z = hλ. Drag the point to choose λ, move the step size, and switch the method. Shaded: |R(z)| ≤ 1. More info: [stability]

λ preset:

z = hλ plane

Shaded: stable for this method. Bold vertical line: the imaginary axis (lossless oscillators).

Solution over 0 ≤ t ≤ 10

Gray: exact Re eλt. Dots: Re yk = Re R(z)k, one dot per step.