Uniform and optimal schemes for stiff initial-value problems (Q1095611)

The author derives conditions for the uniform convergence of some difference schemes for the stiff initial value problem \(\epsilon u'(x)+a(x)u(x)=f(x),\) \(x>0\), u(0) given. These conditions are interpreted in terms of modelling the transient behaviour sufficiently well (fitted schemes). For good behaviour outside the initial layer further conditions are required, and suitable methods are shown to exist. Some numerical comparisons are presented of fitted schemes against backward Euler and trapezoidal rule.