Uniform convergence on a Bakhvalov-type mesh using the preconditioning approach: Technical report [PDF]
, 2015 The linear singularly perturbed convection-diffusion problem in one dimension is considered and its discretization on a Bakhvalov-type mesh is analyzed. The preconditioning technique is used to obtain the pointwise convergence uniform in the perturbation
Nhan, Thái Anh, Vulanović, Relja
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Uniform approximation and explicit estimates for the prolate spheroidal wave functions
, 2014 For fixed $c,$ Prolate Spheroidal Wave Functions (PSWFs), denoted by $\psi_{n, c},$ form an orthogonal basis with remarkable properties for the space of band-limited functions with bandwith $c$.
Bonami, Aline, Karoui, Abderrazek
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A Parallel Method for Population Balance Equations Based on the Method of Characteristics [PDF]
, 2012 In this paper, we present a parallel scheme to solve the population balance equations based on the method of characteristics and the finite element discretization.
Li, Yu, Lin, Qun, Xie, Hehu
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Higher order numerical method for a semilinear system of singularly perturbed differential equations [PDF]
, 2021 In this paper, a system of singularly perturbed second order semilinear differential equations with prescribed boundary conditions is considered. To solve this problem, a parameter-uniform numerical method is constructed which consists of a classical ...
Ayyadurai Tamilselvan +1 more
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A Convergent Scheme for Solving Initial Value Problems with Polynomial and Exponential Functions [PDF]
, 2021 This paper presents the development of a convergent numerical scheme for the solution of initial value problems of first order ordinary differential equations.
Khalil, Sobia +2 more
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Geometry Equilibration of Crystalline Defects in Quantum and Atomistic Descriptions
, 2018 We develop a rigorous framework for modelling the geometry equilibration of crystalline defects. We formulate the equilibration of crystal defects as a variational problems on a discrete energy space and establish qualitatively sharp far-field decay ...
Chen, Huajie +2 more
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Error analysis of trigonometric integrators for semilinear wave equations [PDF]
, 2015 An error analysis of trigonometric integrators (or exponential integrators) applied to spatial semi-discretizations of semilinear wave equations with periodic boundary conditions in one space dimension is given.
Gauckler, Ludwig
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Stiff oscillatory systems, delta jumps and white noise [PDF]
, 1998 Two model problems for stiff oscillatory systems are introduced. Both comprise a linear superposition of N >> 1 harmonic oscillators used as a forcing term for a scalar ODE.
Cano, B. +3 more
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, 2010 In our preceding paper, we have proposed an algorithm for obtaining finite-norm solutions of higher-order linear ordinary differential equations of the Fuchsian type [\sum_m p_m (x) (d/dx)^m] f(x) = 0 (where p_m is a polynomial with rational-number ...
Brenner S.C. +5 more
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Atomic to continuum passage for nanotubes. Part I: a discrete Saint-Venant principle [PDF]
, 2012 We consider general nanotubes of atoms in $\R^3$ where each atom interacts with all others through a two-body potential. When there are no exterior forces, a particular family of nanotubes is the set of perfect nanotubes at the equilibrium. When exterior
El Kass, Danny, Monneau, Régis
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