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On the worst scenario method: Application to a quasilinear elliptic 2D-problem with uncertain coefficients

Petr Harasim (2011)

Applications of Mathematics

We apply a theoretical framework for solving a class of worst scenario problems to a problem with a nonlinear partial differential equation. In contrast to the one-dimensional problem investigated by P. Harasim in Appl. Math. 53 (2008), No. 6, 583–598, the two-dimensional problem requires stronger assumptions restricting the admissible set to ensure the monotonicity of the nonlinear operator in the examined state problem, and, as a result, to show the existence and uniqueness of the state solution....

On those ordinary differential equations that are solved exactly by the improved Euler method

Hans Jakob Rivertz (2013)

Archivum Mathematicum

As a numerical method for solving ordinary differential equations y ' = f ( x , y ) , the improved Euler method is not assumed to give exact solutions. In this paper we classify all cases where this method gives the exact solution for all initial conditions. We reduce an infinite system of partial differential equations for f ( x , y ) to a finite system that is sufficient and necessary for the improved Euler method to give the exact solution. The improved Euler method is the simplest explicit second order Runge-Kutta method....

On time-harmonic Maxwell equations with nonhomogeneous conductivities: Solvability and FE-approximation

Michal Křížek, Pekka Neittaanmäki (1989)

Aplikace matematiky

The solvability of time-harmonic Maxwell equations in the 3D-case with nonhomogeneous conductivities is considered by adapting Sobolev space technique and variational formulation of the problem in question. Moreover, a finite element approximation is presented in the 3D-case together with an error estimate in the energy norm. Some remarks are given to the 2D-problem arising from geophysics.

On total truncation error estimation for the one-step method

Anna Valková (1987)

Aplikace matematiky

In this paper the author establishes estimation of the total truncation error after s steps in the fifth order Ruge-Kutta-Huťa formula for systems of differential equations. The approach is analogous to that used by Vejvoda for the estimation of the classical formulas of the Runge-Kutta type of the 4-th order.

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