Comparing time integrators for parabolic equations in two space dimensions with a mixed derivative

P.J. van der Houwen, B.P. Sommeijer, J.G. Verwer
1979 Journal of Computational and Applied Mathematics  
A numerical comparison is made between three integration methods for semi-discrete parabolic partial differential equations in two space variables with a mixed derivative. Linear as well as nonlinear equations are considered. The integration methods are the well-known one-step line hopscotch method, a four-step line hopscotch method, and a stabilized, explicit Runge-Kutta method. given in [8] . As pointed out by Gourlay & McKee [3], the choice of the second order line hopscotch method is,
more » ... the class of one-step splitting methods, selfevident. The four-step method, of which a second order and a fourth order implementation is considered, is chosen in order to investigate whether this improves the one-step method. The third time integrator, is based on the explicit, stabilized three-step Runge-Kutta formulas from [9] . By comparing this explicit method (*) P.
doi:10.1016/0771-050x(79)90001-9 fatcat:awuegvbatrdolhq4dzzzoy6qzy