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The virtual element method for eigenvalue problems with potential terms on polytopic meshes

Ondřej Čertík, Francesca Gardini, Gianmarco Manzini, Giuseppe Vacca (2018)

Applications of Mathematics

We extend the conforming virtual element method (VEM) to the numerical resolution of eigenvalue problems with potential terms on a polytopic mesh. An important application is that of the Schrödinger equation with a pseudopotential term. This model is a fundamental element in the numerical resolution of more complex problems from the Density Functional Theory. The VEM is based on the construction of the discrete bilinear forms of the variational formulation through certain polynomial projection operators...

Time discretizations for evolution problems

Miloslav Vlasák (2017)

Applications of Mathematics

The aim of this work is to give an introductory survey on time discretizations for liner parabolic problems. The theory of stability for stiff ordinary differential equations is explained on this problem and applied to Runge-Kutta and multi-step discretizations. Moreover, a natural connection between Galerkin time discretizations and Runge-Kutta methods together with order reduction phenomenon is discussed.

Toward a two-step Runge-Kutta code for nonstiff differential systems

Zbigniew Bartoszewski, Zdzisław Jackiewicz (2001)

Applicationes Mathematicae

Various issues related to the development of a new code for nonstiff differential equations are discussed. This code is based on two-step Runge-Kutta methods of order five and stage order five. Numerical experiments are presented which demonstrate that the new code is competitive with the Matlab ode45 program for all tolerances.

Transfer of boundary conditions for Poisson's equation on a circle

Jiří Taufer, Emil Vitásek (1994)

Applications of Mathematics

The method of transfer of boundary conditions yields a universal frame into which most methods for solving boundary value problems for ordinary differential equations can be included. The purpose of this paper is to show a possibility to extend the idea of transfer of conditions to a particular twodimensional problem.

Transfer of conditions for singular boundary value problems

Petr Přikryl, Jiří Taufer, Emil Vitásek (1989)

Aplikace matematiky

Numerical solution of linear boundary value problems for ordinary differential equations by the method of transfer of conditions consists in replacing the problem under consideration by a sequence of initial value problems. The method of transfer for systems of equations of the first order with Lebesque integrable coefficients was studied by one of the authors before. The purpose of this paper is to extend the idea of the transfer of conditions to singular boundary value problems for a linear second-order...

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