A decaying quantity obeys with .

PHYSICS · Multi-part · Fermi University Physics · Mathematical Methods for Physics · Numerical and computational mathematics · Numerical and computational mathematics

Error, Chance and the Machine, Ch Ordinary differential equations: order, stability and stiffness

Problem

A decaying quantity obeys

y' = \lambda y

with

\lambda = -50\,\mathrm{s^{-1}}

. ((a)) Find the largest step

h

for which forward Euler's method is linearly stable on this equation. ((b)) State whether backward Euler suffers any such step restriction, and give the value of its stability function

R(z)

z \to -\infty

, explaining what this value means for a fast-decaying component.

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