Über die Konvergenzgeschwindigkeit projektiver Verfahren. II.
Unconditional stability of difference formulas
The paper concerns the solution of partial differential equations of evolution type by the finite difference method. The author discusses the general assumptions on the original equation as well as its discretization, which guarantee that the difference scheme is unconditionally stable, i.e. stable without any stability condition for the time-step. A new notion of the -acceptability of the integration formula is introduced and examples of such formulas are given. The results can be applied to ordinary...
Uniformly convergent adaptive methods for a class of parametric operator equations∗
We derive and analyze adaptive solvers for boundary value problems in which the differential operator depends affinely on a sequence of parameters. These methods converge uniformly in the parameters and provide an upper bound for the maximal error. Numerical computations indicate that they are more efficient than similar methods that control the error in a mean square sense.
Uniformly convergent adaptive methods for a class of parametric operator equations∗
We derive and analyze adaptive solvers for boundary value problems in which the differential operator depends affinely on a sequence of parameters. These methods converge uniformly in the parameters and provide an upper bound for the maximal error. Numerical computations indicate that they are more efficient than similar methods that control the error in a mean square sense.
Universality of the best determined terms method
The properties are studied of the best determined terms method with respect to an a priori decomposition . The universal approximation to the normal solution of the first kind Fredholm integral equation is found.