Stability and convergence of discretisations of initial value p.d.e.'s - Giles, M (Unspecified, 1996)
This paper examines the stability and convergence of discretisations of initial value p.d.e.'s using spatial discretisation followed by time integration with an explicit one-step method. A Cauchy integral representation is used to bound the growth in the discrete solution. New results are obtained regarding sufficient conditions for both algebraic and strong stability. Sufficient conditions are also derived for convergence on a finite time interval.