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Lagrangian and moving mesh methods for the convection diffusion equation

Konstantinos Chrysafinos, Noel J. Walkington (2008)

ESAIM: Mathematical Modelling and Numerical Analysis

We propose and analyze a semi Lagrangian method for the convection-diffusion equation. Error estimates for both semi and fully discrete finite element approximations are obtained for convection dominated flows. The estimates are posed in terms of the projections constructed in [Chrysafinos and Walkington, SIAM J. Numer. Anal. 43 (2006) 2478–2499; Chrysafinos and Walkington, SIAM J. Numer. Anal. 44 (2006) 349–366] and the dependence of various constants upon the diffusion parameter is ...

Lagrangian approach to deriving energy-preserving numerical schemes for the Euler–Lagrange partial differential equations

Takaharu Yaguchi (2013)

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

We propose a Lagrangian approach to deriving energy-preserving finite difference schemes for the Euler–Lagrange partial differential equations. Noether’s theorem states that the symmetry of time translation of Lagrangians yields the energy conservation law. We introduce a unique viewpoint on this theorem: “the symmetry of time translation of Lagrangians derives the Euler–Lagrange equation and the energy conservation law, simultaneously.” The proposed method is a combination of a discrete counter...

Lagrangian evolution approach to surface-patch quadrangulation

Martin Húska, Matej Medl'a, Karol Mikula, Serena Morigi (2021)

Applications of Mathematics

We present a method for the generation of a pure quad mesh approximating a discrete manifold of arbitrary topology that preserves the patch layout characterizing the intrinsic object structure. A three-step procedure constitutes the core of our approach which first extracts the patch layout of the object by a topological partitioning of the digital shape, then computes the minimal surface given by the boundaries of the patch layout (basic quad layout) and then evolves it towards the object boundaries....

Laguerre polynomials in the inversion of Mellin transform

George J. Tsamasphyros, Pericles S. Theocaris (1981)

Aplikace matematiky

In order to use the well known representation of the Mellin transform as a combination of two Laplace transforms, the inverse function g ( r ) is represented as an expansion of Laguerre polynomials with respect to the variable t = l n r . The Mellin transform of the series can be written as a Laurent series. Consequently, the coefficients of the numerical inversion procedure can be estimated. The discrete least squares approximation gives another determination of the coefficients of the series expansion. The last...

Lanczos-like algorithm for the time-ordered exponential: The * -inverse problem

Pierre-Louis Giscard, Stefano Pozza (2020)

Applications of Mathematics

The time-ordered exponential of a time-dependent matrix 𝖠 ( t ) is defined as the function of 𝖠 ( t ) that solves the first-order system of coupled linear differential equations with non-constant coefficients encoded in 𝖠 ( t ) . The authors have recently proposed the first Lanczos-like algorithm capable of evaluating this function. This algorithm relies on inverses of time-dependent functions with respect to a non-commutative convolution-like product, denoted by * . Yet, the existence of such inverses, crucial to...

Laplace Adomian decomposition method for solving a fish farm model

M. Sambath, K. Balachandran (2016)

Nonautonomous Dynamical Systems

In this work, a combined form of the Laplace transform method and the Adomian decomposition method is implemented to give an approximate solution of nonlinear systems of differential equations such as fish farm model with three components nutrient, fish and mussel. The technique is described and illustrated with a numerical example.

Laplace-Stieltjes transform of the system mean lifetime via geometric process model

Gökhan Gökdere, Mehmet Gürcan (2016)

Open Mathematics

Operation principle of the engineering systems occupies an important role in the reliability theory. In most of the studies, the reliability function of the system is obtained analytically according to the structure of the system. Also in such studies the mean operating time of the system is calculated. However, the reliability function of some systems, such as repairable system, cannot be easily obtained analytically. In this case, forming Laplace-Stieltjes transform of the system can provide a...

Large-scale nonlinear programming algorithm using projection methods

Paweł Białoń (2000)

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

A method for solving large convex optimization problems is presented. Such problems usually contain a big linear part and only a small or medium nonlinear part. The parts are tackled using two specialized (and thus efficient) external solvers: purely nonlinear and large-scale linear with a quadratic goal function. The decomposition uses an alteration of projection methods. The construction of the method is based on the zigzagging phenomenon and yields a non-asymptotic convergence, not dependent...

Currently displaying 41 – 60 of 195