Due to the fundamental role of differential equations in science and engineering it has long
been a basic task of numerical analysts to generate numerical values of solutions to …

As Tikhonov and Samarskiĭ showed for $ k= 2$, it is not essential that kth-order compact
difference schemes be centered at the arithmetic mean of the stencil's points to yield second …

Hauptziel des vorliegenden zweiten Teils der Numerik von An fangswertaufgaben
gewöhnlicher Differentialgleichungen ist es, die heute zur Verfügung stehenden Verfahren …

Multistep predictor-corrector methods are commonly used for the numerical solution of
ordinary differential equations. In its simplest form, ak-step method with accuracy of order …

In this paper a drift-randomized Milstein method is introduced for the numerical solution of
non-autonomous stochastic differential equations with non-differentiable drift coefficient …

Let α\leqqa<b be real numbers and let C(t_1,t_2→E^n) denote the space of continuous
functions on t_1,t_2 into E^n (n-dimensional Euclidean space). We consider the Cauchy …

The Lax-Richtmyer theorem is extended to work in the framework of Stetter's theory of
discretizations. The new result applies to both initial and boundary value problems …

We present an abstract concept for the error analysis of numerical schemes for semilinear
stochastic partial differential equations (SPDEs) and demonstrate its usefulness by proving …

The cell-vertex formulation of the finite volume method has been developed and widely used
to model inviscid flows in aerodynamics: more recently, one of us has proposed an …

In this paper the numerical solution of nonautonomous semilinear stochastic evolution
equations driven by an additive Wiener noise is investigated. We introduce a novel fully …