Summary: NUMERICAL STABILITY;
When solving the initial value problem
Y 0(x) = f(x; Y (x)); x0 x b
Y (x0) = Y0
we know that small changes in the initial data Y0 will
result in small changes in the solution of the di eren-
tial equation. More precisely, consider the perturbed
"(x) = f(x; Y"(x)); x0 x b
Y"(x0) = Y0 + "
Then assuming f(x; z) and @f(x; z)=@z are continu-
ous for x0 x b; 1 < z < 1, we have
x0 x b
jY"(x) Y (x)j c j"j
for some constant c > 0. We would like our numerical
methods to have a similar property.
Consider the Euler method