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The CUDA implementation of the method of lines for the curvature dependent flows

Tomáš Oberhuber, Atsushi Suzuki, Vítězslav Žabka (2011)

Kybernetika

We study the use of a GPU for the numerical approximation of the curvature dependent flows of graphs - the mean-curvature flow and the Willmore flow. Both problems are often applied in image processing where fast solvers are required. We approximate these problems using the complementary finite volume method combined with the method of lines. We obtain a system of ordinary differential equations which we solve by the Runge-Kutta-Merson solver. It is a robust solver with an automatic choice of the...

The Rothe method and time periodic solutions to the Navier-Stokes equations and equations of magnetohydrodynamics

Dana Lauerová (1990)

Aplikace matematiky

The existence of a periodic solution of a nonlinear equation z ' + A 0 z + B 0 z = F is proved. The theory developed may be used to prove the existence of a periodic solution of the variational formulation of the Navier-Stokes equations or the equations of magnetohydrodynamics. The proof of the main existence theorem is based on Rothe method in combination with the Galerkin method, using the Brouwer fixed point theorem.

The Rothe method for the McKendrick-von Foerster equation

Henryk Leszczyński, Piotr Zwierkowski (2013)

Czechoslovak Mathematical Journal

We present the Rothe method for the McKendrick-von Foerster equation with initial and boundary conditions. This method is well known as an abstract Euler scheme in extensive literature, e.g. K. Rektorys, The Method of Discretization in Time and Partial Differential Equations, Reidel, Dordrecht, 1982. Various Banach spaces are exploited, the most popular being the space of bounded and continuous functions. We prove the boundedness of approximate solutions and stability of the Rothe method in L ∞ and...

The use of linear approximation scheme for solving the Stefan problem

Peter Dzurenda (1997)

Applications of Mathematics

This paper deals with the linear approximation scheme to approximate a singular parabolic problem: the two-phase Stefan problem on a domain consisting of two components with imperfect contact. The results of some numerical experiments and comparisons are presented. The method was used to determine the temperature of steel in the process of continuous casting.

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