Results 31 to 40 of about 3,166 (168)

Uniformly convergent numerical method for time-fractional convection–diffusion equation with variable coefficients

Partial Differential Equations in Applied Mathematics, 2023
This paper presents a uniformly convergent numerical scheme for singularly perturbed fractional order convection–diffusion equations with variable coefficients. First, the time-fractional derivative is considered in the Caputo sense and treated using the
Worku Tilahun Aniley, Gemechis File Duressa   +1 more
doaj   +1 more source

Reduced Order Modelling of Shigesada-Kawasaki-Teramoto Cross-Diffusion Systems

Journal of Mathematical Sciences and Modelling, 2023
Shigesada-Kawasaki-Teramoto (SKT) is the most known equation in population ecology for nonlinear cross-diffusion systems. The full order model (FOM) of the SKT system is constructed using symmetric interior penalty discontinuous Galerkin method (SIPG ...
Gülden Mülayim
doaj   +1 more source

IIET: Efficient Numerical Transformer via Implicit Iterative Euler Method

Proceedings of the 2025 Conference on Empirical Methods in Natural Language Processing
High-order numerical methods enhance Transformer performance in tasks like NLP and CV, but introduce a performance-efficiency trade-off due to increased computational overhead. Our analysis reveals that conventional efficiency techniques, such as distillation, can be detrimental to the performance of these models, exemplified by PCformer.
Liu, Xinyu, Li, Bei, Liu, Jiahao, Ruan, Junhao, Jiao, Kechen, Tang, Hongyin, Wang, Jingang, Tong, Xiao, Zhu, Jingbo   +8 more
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Numerical Solution of Anisotropic Diffusion with Localized Source Using Euler Scheme and Finite Element Method

Berkala Sainstek
This study investigates the numerical modeling of two-dimensional anisotropic diffusion processes involving a spatially localized and temporally limited energy or thermal source.
M. Ziaul Arif, Millatuz Zahroh, Sailah Ar Rizka   +2 more
doaj   +1 more source

Convergence analysis of the semi-implicit euler method for abstract evolution equations [PDF]

Numerical Functional Analysis and Optimization, 1995
The semi-implicit Euler discretization method is studied for abstract evolution equations in a Hilbert space H, like , where f(t,•,v) is one-sided Lipschitz and sufficiently small, and f(t u, •) is Lipschitz-continuous. Extension to Banach spaces is then pointed out.
SPIGLER R, VIANELLO, MARCO
openaire   +3 more sources

The Spectral Method for the Cahn-Hilliard Equation with Concentration-Dependent Mobility

Journal of Applied Mathematics, 2012
This paper is concerned with the numerical approximations of the Cahn-Hilliard-type equation with concentration-dependent mobility. Convergence analysis and error estimates are presented for the numerical solutions based on the spectral method for the ...
Shimin Chai, Yongkui Zou
doaj   +1 more source

The implementation of the mortar spectral element discretization of the heat equation with discontinuous diffusion coefficient

Boundary Value Problems, 2019
We propose to implement the mortar spectral elements discretization of the heat equation in a bounded two-dimensional domain with a piecewise continuous diffusion coefficient. The discretization on time is based on the Euler implicit method.
Mohamed Abdelwahed, Nejmeddine Chorfi
doaj   +1 more source

Numerical schemes for 3D parabolic problem with non-local boundwy condition

Lietuvos Matematikos Rinkinys, 2004
Two finite difference schemes are used to solve the 3D parabolic problem with a non-local boundary condition. A new approximation of the initial condition is proposed for the explicit Euler scheme.
Raimondas Čiegis, Mečislovas Meilūnas, Olga Subač   +2 more
doaj   +3 more sources

Hybrid method for singularly perturbed Robin type parabolic convection–diffusion problems on Shishkin mesh

Partial Differential Equations in Applied Mathematics, 2023
This work presents a numerical solution to singularly perturbed Robin-type parabolic convection–diffusion problems. A hybrid method that combines the central difference scheme in the inner region and the midpoint of the upwind scheme in the outer region ...
Fasika Wondimu Gelu, Gemechis File Duressa   +1 more
doaj   +1 more source

A preconditioned iterative solution scheme for nonlinear parabolic systems arising in air pollution modeling

Mathematical Modelling and Analysis, 2013
A preconditioned iterative solution method is presented for nonlinear parabolic transport systems. The ingredients are implicit Euler discretization in time and finite element discretization in space, then an outer-inner (outer damped inexact Newton ...
Janos Karatson, Tamas Kurics
doaj   +1 more source