Results 31 to 40 of about 96 (92)

A semidiscrete scheme for evolution equations with memory

Discrete and Continuous Dynamical Systems, 2019
We introduce a new mathematical framework for the time discretization of evolution equations with memory. As a model, we focus on an abstract version of the equation partial derivative(t)u(t) - integral(infinity)(0) g(s)Delta u(t - s) ds = 0 with Dirichlet boundary conditions, modeling hereditary heat conduction with Gurtin-Pipkin thermal law.
Dell'Oro, Filippo, Goubet, Olivier, Mammeri, Youcef, Pata, Vittorino   +3 more
openaire   +3 more sources

Hyperbolic relaxation of the viscous Cahn–Hilliard equation with a symport term for biological applications

Mathematical Methods in the Applied Sciences, Volume 47, Issue 7, Page 5999-6035, 15 May 2024.
We consider the hyperbolic relaxation of the viscous Cahn–Hilliard equation with a symport term. This equation is characterized by the presence of the additional inertial term τDϕtt$$ {\tau}_D{\phi}_{tt} $$ that accounts for the relaxation of the diffusion flux.
Dieunel Dor, Alain Miranville, Morgan Pierre   +2 more
wiley   +1 more source

Modeling and simulation of the input–output behavior of a geothermal energy storage

Mathematical Methods in the Applied Sciences, Volume 47, Issue 1, Page 371-396, 15 January 2024.
This paper investigates mathematical modeling and numerical methods for simulations of the input–output behavior of a geothermal energy storage. Such simulations are needed for the optimal control and management of residential heating systems equipped with an underground thermal storage. There, a given volume under or aside of a building is filled with
Paul Honore Takam, Ralf Wunderlich, Olivier Menoukeu Pamen   +2 more
wiley   +1 more source

Why diffusion‐based preconditioning of Richards equation works: Spectral analysis and computational experiments at very large scale

Numerical Linear Algebra with Applications, Volume 31, Issue 1, January 2024.
Abstract We consider here a cell‐centered finite difference approximation of the Richards equation in three dimensions, averaging for interface values the hydraulic conductivity K=K(p)$$ K=K(p) $$, a highly nonlinear function, by arithmetic, upstream and harmonic means.
Daniele Bertaccini, Pasqua D'Ambra, Fabio Durastante, Salvatore Filippone   +3 more
wiley   +1 more source

Stage‐parallel preconditioners for implicit Runge–Kutta methods of arbitrarily high order, linear problems

Numerical Linear Algebra with Applications, Volume 31, Issue 1, January 2024.
Abstract Fully implicit Runge–Kutta methods offer the possibility to use high order accurate time discretization to match space discretization accuracy, an issue of significant importance for many large scale problems of current interest, where we may have fine space resolution with many millions of spatial degrees of freedom and long time intervals ...
Owe Axelsson, Ivo Dravins, Maya Neytcheva   +2 more
wiley   +1 more source

Parameter‐Uniform Convergent Numerical Approach for Time‐Fractional Singularly Perturbed Partial Differential Equations With Large Time Delay

Computational and Mathematical Methods, Volume 2024, Issue 1, 2024.
In this study, we consider a parameter‐uniform convergent numerical approach for a class of time‐fractional singularly perturbed partial differential equations (TF‐SPDPDEs) with large delay in time that exhibits a regular exponential boundary layer on the right side of the spatial domain.
Habtamu Getachew Kumie, Awoke Andargie Tiruneh, Getachew Adamu Derese, Higinio Ramos   +3 more
wiley   +1 more source

Conservative Semidiscrete Difference Schemes for Timoshenko Systems [PDF]

Journal of Applied Mathematics, 2014
We present a parameterized family of finite-difference schemes to analyze the energy properties for linearly elastic constant-coefficient Timoshenko systems considering shear deformation and rotatory inertia. We derive numerical energies showing the positivity, and the energy conservation property and we show how to avoid a numerical anomaly known as ...
openaire   +4 more sources

An Unconditionally Stable Numerical Method for Space Tempered Fractional Convection‐Diffusion Models

Journal of Mathematics, Volume 2024, Issue 1, 2024.
A second‐order numerical method for two‐sided tempered fractional convection‐diffusion equations is studied in this paper, both convection term and diffusion term are approximated by the tempered weighted and shifted Grünwald difference operators, the first time partial derivative is discretized by the Crank–Nicolson method, and then a class of second ...
Zeshan Qiu, Xian-Ming Gu
wiley   +1 more source

An Efficient Local Artificial Boundary Condition for Infinite Long Finite Element Euler–Bernoulli Beam

Shock and Vibration, Volume 2024, Issue 1, 2024.
To solve the wave propagation problems of the Euler–Bernoulli beam in an unbounded domain effectively and efficiently, a new local artificial boundary condition technology is proposed. It replaces the residual right‐hand side of the truncated discrete equation with an equivalent linear algebraic system.
Zijun Zheng, Gang Pang, Gerardo Silva-Navarro   +2 more
wiley   +1 more source

Fitted Tension Spline Scheme for a Singularly Perturbed Parabolic Problem With Time Delay

Journal of Applied Mathematics, Volume 2024, Issue 1, 2024.
A fitted tension spline numerical scheme for a singularly perturbed parabolic problem (SPPP) with time delay is proposed. The presence of a small parameter ε as a multiple of the diffusion term leads to the suddenly changing behaviors of the solution in the boundary layer region.
Sisay Ketema Tesfaye, Gemechis File Duressa, Tekle Gemechu Dinka, Mesfin Mekuria Woldaregay, Tudor Barbu   +4 more
wiley   +1 more source