We address the question of convergence of fully discrete Runge-Kutta approximations. We
prove that, under certain conditions, the order in time of the fully discrete scheme equals the …

The main goal of this paper is to show that discrete mollification is a simple and effective way
to speed up explicit time-stepping schemes for partial differential equations. The second …

We construct and analyse explicit methods for solving initial value problems for systems of
differential equations with expensive right-hand side functions whose Jacobian has its stiff …

The shallow water wave equation is derived in a general deforming co‐ordinate system. A
weak form is developed which displays the natural boundary condition prominently and …

The discrete mollification method is a data smoothing procedure, based on convolution, that
is appropriate for the stabilization of explicit schemes for the numerical solution of partial …

Smoothing techniques have been used for stabilizing explicit time integration of parabolic
and hyperbolic initial‐boundary value problems. Similar techniques can be used for the …

Residue smoothing is usually applied in order to accelerate the convergence of iteration
processes. Here, we show that residue smoothing can also be used in order to increase the …

Smoothing techniques are frequently applied in the numerical solution of (initial-) boundary-
value problems for partial differential equations. Usually, the smoothing procedure consists …

Implicit step-by-step methods for numerically solving the initial-value problem {y′= f (y), y
(0)= y 0} usually lead to implicit relations of which the Jacobian can be approximated by a …

En este trabaXo se define la molificación discreta, se presentan los principales estima $ dos
asociados con aproximación de funciones y sus derivadas y se aplica el método a dos …