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Computational studies of conserved mean-curvature flow

Miroslav Kolář, Michal Beneš, Daniel Ševčovič (2014)

Mathematica Bohemica

The paper presents the results of numerical solution of the evolution law for the constrained mean-curvature flow. This law originates in the theory of phase transitions for crystalline materials and describes the evolution of closed embedded curves with constant enclosed area. It is reformulated by means of the direct method into the system of degenerate parabolic partial differential equations for the curve parametrization. This system is solved numerically and several computational studies are...

Computational studies of non-local anisotropic Allen-Cahn equation

Michal Beneš, Shigetoshi Yazaki, Masato Kimura (2011)

Mathematica Bohemica

The paper presents the results of numerical solution of the Allen-Cahn equation with a non-local term. This equation originally mentioned by Rubinstein and Sternberg in 1992 is related to the mean-curvature flow with the constraint of constant volume enclosed by the evolving curve. We study this motion approximately by the mentioned PDE, generalize the problem by including anisotropy and discuss the computational results obtained.

Computational technique for treating the nonlinear Black-Scholes equation with the effect of transaction costs

Hitoshi Imai, Naoyuki Ishimura, Hideo Sakaguchi (2007)

Kybernetika

We deal with numerical computation of the nonlinear partial differential equations (PDEs) of Black–Scholes type which incorporate the effect of transaction costs. Our proposed technique surmounts the difficulty of infinite domains and unbounded values of the solutions. Numerical implementation shows the validity of our scheme.

Concentration in the Nonlocal Fisher Equation: the Hamilton-Jacobi Limit

Benoît Perthame, Stephane Génieys (2010)

Mathematical Modelling of Natural Phenomena

The nonlocal Fisher equation has been proposed as a simple model exhibiting Turing instability and the interpretation refers to adaptive evolution. By analogy with other formalisms used in adaptive dynamics, it is expected that concentration phenomena (like convergence to a sum of Dirac masses) will happen in the limit of small mutations. In the present work we study this asymptotics by using a change of variables that leads to a constrained Hamilton-Jacobi equation. We prove the convergence analytically...

Conservation schemes for convection-diffusion equations with Robin boundary conditions

Stéphane Flotron, Jacques Rappaz (2013)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

In this article, we present a numerical scheme based on a finite element method in order to solve a time-dependent convection-diffusion equation problem and satisfy some conservation properties. In particular, our scheme is able to conserve the total energy for a heat equation or the total mass of a solute in a fluid for a concentration equation, even if the approximation of the velocity field is not completely divergence-free. We establish a priori errror estimates for this scheme and we give some...

Consistent models for electrical networks with distributed parameters

Corneliu A. Marinov, Gheorghe Moroşanu (1992)

Mathematica Bohemica

A system of one-dimensional linear parabolic equations coupled by boundary conditions which include additional state variables, is considered. This system describes an electric circuit with distributed parameter lines and lumped capacitors all connected through a resistive multiport. By using the monotony in a space of the form L 2 ( 0 , T ; H 1 ) , one proves the existence and uniqueness of a variational solution, if reasonable engineering hypotheses are fulfilled.

Consistent stable difference schemes for nonlinear Black-Scholes equations modelling option pricing with transaction costs

Rafael Company, Lucas Jódar, José-Ramón Pintos (2009)

ESAIM: Mathematical Modelling and Numerical Analysis

This paper deals with the numerical solution of nonlinear Black-Scholes equation modeling European vanilla call option pricing under transaction costs. Using an explicit finite difference scheme consistent with the partial differential equation valuation problem, a sufficient condition for the stability of the solution is given in terms of the stepsize discretization variables and the parameter measuring the transaction costs. This stability condition is linked to some properties of the numerical...

Construction of a natural norm for the convection-diffusion-reaction operator

Giancarlo Sangalli (2004)

Bollettino dell'Unione Matematica Italiana

In this work, we construct, by means of the function space interpolation theory, a natural norm for a generic linear coercive and non-symmetric operator. We look for a norm which is the counterpart of the energy norm for symmetric operators. The natural norm allows for continuity and inf-sup conditions independent of the operator. Particularly we consider the convection-diffusion-reaction operator, for which we obtain continuity and inf-sup conditions that are uniform with respect to the operator...

Currently displaying 61 – 80 of 178