Results 11 to 20 of about 1,325 (149)
Method of semidiscretization in time for quasilinearintegrodifferential equations [PDF]
International Journal of Mathematics and Mathematical Sciences, 2004 We consider a class of quasilinear integrodifferential equations in a reflexive Banach space. We apply the method of semidiscretization in time to establish the existence, uniqueness, and continuous dependence on the initial data of strong solutions.
D. Bahuguna, Reeta Shukla
doaj +2 more sources
Semidiscrete Vortex Solitons [PDF]
Advanced Photonics Research, 2021 A possibility of creation of stable optical solitons combining one continuous and one discrete coordinates, with embedded vorticity, in an array of planar waveguides with intrinsic cubic–quintic (CQ) nonlinearity is demonstrated. The same system may be realized in terms of the spatiotemporal light propagation in an array of tunnel‐coupled optical ...
Xiaoxi Xu +6 more
openaire +3 more sources
Semidiscretization for a nonlocal parabolic problem [PDF]
International Journal of Mathematics and Mathematical Sciences, 2005 A time discretization technique by Euler forward scheme is proposed to deal with a nonlocal parabolic problem. Existence and uniqueness of the approximate solution are proved.
Abderrahmane El Hachimi +1 more
doaj +3 more sources
Semidiscrete Quantum Droplets and Vortices [PDF]
Physical Review Letters, 2019 We consider a binary bosonic condensate with weak mean-field (MF) residual repulsion, loaded in an array of nearly one-dimensional traps coupled by transverse hopping. With the MF force balanced by the effectively one-dimensional attraction, induced in each trap by the Lee-Hung-Yang correction (produced by quantum fluctuations around the MF state ...
Xiliang Zhang +7 more
openaire +3 more sources
Study of Solutions to a Fourth Order Parabolic Equation∗
Mathematical Modelling and Analysis, 2016 This paper studies a fourth-order parabolic equation ut + ε(unuxxx)x − δ|uxx|muxx = 0 with the boundary conditions uxx = 0, u = l and the initial condition u(x, 0) = u0(x). The existence of solutions is obtained from the semidiscretization method.
Bo Liang, Xiting Peng, Huiying Shen
doaj +1 more source
Variational Laplacians for semidiscrete surfaces [PDF]
Advances in Computational Mathematics, 2016 The authors propose a variational definition of the Laplacian on semidiscrete surfaces. Recall that the classical Laplace-Beltrami operator on Riemannian manifolds can be defined via the Dirichlet energy functional with an obvious connection to the mean curvature normal vector.
Carl, Wolfgang, Wallner, Johannes
openaire +3 more sources
ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik, Volume 103, Issue 11, November 2023., 2023 We consider partitioned time integration for heterogeneous coupled heat equations. First and second order multirate, as well as time‐adaptive Dirichlet‐Neumann Waveform relaxation (DNWR) methods are derived. In 1D and for implicit Euler time integration, we analytically determine optimal relaxation parameters for the fully discrete scheme.
Peter Meisrimel +2 more
wiley +1 more source
Stability of Systems with Stochastic Delays and Applications to Genetic Regulatory Networks [PDF]
, 2016 The dynamics of systems with stochastically varying time delays are investigated in this paper. It is shown that the mean dynamics can be used to derive necessary conditions for the stability of equilibria of the stochastic system.
Bennett, Matthew R. +4 more
core +2 more sources
Sobolev‐orthogonal systems with tridiagonal skew‐Hermitian differentiation matrices
Studies in Applied Mathematics, Volume 150, Issue 2, Page 420-447, February 2023., 2023 Abstract We introduce and develop a theory of orthogonality with respect to Sobolev inner products on the real line for sequences of functions with a tridiagonal, skew‐Hermitian differentiation matrix. While a theory of such L2 ‐orthogonal systems is well established, Sobolev orthogonality requires new concepts and their analysis.
Arieh Iserles, Marcus Webb
wiley +1 more source
Accuracy Bounds for Semidiscretizations of Hyperbolic Problems [PDF]
Mathematics of Computation, 1985 Bounds are given for the error constant of stable finite-difference methods for first-order hyperbolic equations in one space dimension, which use r downwind and s upwind points in the discretization of the space derivatives, and which are of optimal order p = min ( r + s , 2 r
Jeltsch, Rolf, Strack, Klaus-Günther
openaire +2 more sources