Results 61 to 70 of about 4,597 (168)

Spline Collocation for Multi-Term Fractional Integro-Differential Equations with Weakly Singular Kernels

Fractal and Fractional, 2021
We consider general linear multi-term Caputo fractional integro-differential equations with weakly singular kernels subject to local or non-local boundary conditions.
Arvet Pedas, Mikk Vikerpuur
doaj   +1 more source

A Chemo‐Damage‐Mechanical Coupled Phase‐Field Model for Three‐Dimensional Hydrogen‐Assisted Dynamic Cracking

International Journal for Numerical Methods in Engineering, Volume 126, Issue 8, 30 April 2025.
ABSTRACT This study develops a chemo‐damage‐mechanical coupled phase‐field method for modeling two‐dimensional and/or three‐dimensional hydrogen‐assisted transient dynamic cracking in metallic materials. In this method, hydrogen diffusion in solids is described by the evolution of bulk hydrogen concentration governed by the diffusion equation with an ...
Hui Li, Shanyong Wang
wiley   +1 more source

High-Order Energy and Linear Momentum Conserving Methods for the Klein-Gordon Equation

Mathematics, 2018
The Klein-Gordon equation is a model for free particle wave function in relativistic quantum mechanics. Many numerical methods have been proposed to solve the Klein-Gordon equation. However, efficient high-order numerical methods that preserve energy and
He Yang
doaj   +1 more source

Interior a posteriori error estimates for time discrete approximations of parabolic problems [PDF]

, 2012
a posteriori error estimates for time discrete approximations ...
Charalambos Makridakis, Charalambos Makridakis, Christian Lubich, Christian Lubich   +3 more
core   +1 more source

An X‐FFT Solver for Two‐Dimensional Thermal Homogenization Problems

International Journal for Numerical Methods in Engineering, Volume 126, Issue 7, 15 April 2025.
ABSTRACT We introduce an approach to computational homogenization which unites the accuracy of interface‐conforming finite elements (FEs) and the computational efficiency of methods based on the fast Fourier transform (FFT) for two‐dimensional thermal conductivity problems.
Flavia Gehrig, Matti Schneider
wiley   +1 more source

Linear/linear rational spline interpolation

Mathematical Modelling and Analysis, 2010
For a strictly monotone function y on [a, b] we describe the construction of an interpolating linear/linear rational spline S of smoothness class C 1. We show that for the linear/linear rational splines we obtain ¦S(xi ) − y(xi )¦8 = O(h 4) on uniform ...
Erge Ideon, Peeter Oja
doaj   +1 more source

Unconditional superconvergence analysis of an energy-stable finite element scheme for nonlinear Benjamin–Bona–Mahony–Burgers equation

Boundary Value Problems, 2022
In this paper, an energy-stable Crank–Nicolson fully discrete finite element scheme is proposed for the Benjamin–Bona–Mahony–Burgers equation. Firstly, the stability of energy is proved, which leads to the boundedness of the finite element solution in H ...
Lele Wang, Xin Liao, Huaijun Yang
doaj   +1 more source

Superconvergence Relations

, 2001
For a limited number of matter fields, the discontinuity of the transverse gauge field propagator can satisfy an exact sum rule. With controlled and limited gauge dependence, this supercconvergence relation is of physical interest.
openaire   +2 more sources

Convergence of Damped Polarization Schemes for the FFT‐Based Computational Homogenization of Inelastic Media With Pores

International Journal for Numerical Methods in Engineering, Volume 126, Issue 3, 15 February 2025.
ABSTRACT Porous microstructures represent a challenge for the convergence of FFT‐based computational homogenization methods. In this contribution, we show that the damped Eyre–Milton iteration is linearly convergent for a class of nonlinear composites with a regular set of pores, provided the damping factor is chosen between zero and unity.
Elodie Donval, Matti Schneider
wiley   +1 more source

A Class of Higher‐Order Collocation Scheme for the Integral Equation of the Convolution Type

Journal of Mathematics, Volume 2025, Issue 1, 2025.
Auto convolution Volterra integral equations (ACVIEs) are the particular form of non‐standard integral equations arising in mathematical modeling processes and the computation of certain functions. In this paper, a novel class of multistep collocation methods (NM‐SCMs) is constructed in order to find a higher‐order method is constructed for the ...
M. Alsahlanee, P. Darania, S. Pishbin, Xian-Ming Gu   +3 more
wiley   +1 more source