Fifth-order Runge-Kutta with higher order derivative approximations.
Fourth order time-stepping for low dispersion Korteweg-de Vries and nonlinear Schrödinger equations.
Fully discrete error estimation by the method of lines for a nonlinear parabolic problem
A posteriori error estimates for a nonlinear parabolic problem are introduced. A fully discrete scheme is studied. The space discretization is based on a concept of hierarchical finite element basis functions. The time discretization is done using singly implicit Runge-Kutta method (SIRK). The convergence of the effectivity index is proven.