In this paper a technique is suggested to integrate linear initial boundary value problems with exponential quadrature rules in such a way that the order in time is as high as possible.
A thorough error analysis is given for both the classical approach of integrating the problem rstly in space and then in time and of doing it in the reverse order in a suitable manner. Time-dependent
boundary conditions are considered with both approaches and full discretization formulas are given
to implement the methods once the quadrature nodes have been chosen for the time integration
and a particular (although very general) scheme is selected for the space discretization. Numerical
experiments are shown which corroborate that, for example, with the suggested technique, order 2s
is obtained when choosing the s nodes of Gaussian quadrature rule.
