Results 21 to 30 of about 520 (46)

The Initial Value Problem for Weakly Nonlinear PDE

, 2014
We will discuss an extension of the pseudospectral method developed by Wineberg, McGrath, Gabl, and Scott for the numerical integration of the KdV initial value problem.
Palais, Richard S.
core   +1 more source

To be or not to be intrusive? The solution of parametric and stochastic equations - the "plain vanilla" Galerkin case [PDF]

, 2013
In parametric equations - stochastic equations are a special case - one may want to approximate the solution such that it is easy to evaluate its dependence of the parameters.
Giraldi, Loïc, Litvinenko, Alexander, Liu, Dishi, Matthies, Hermann G., Matthies, Hermann,, Nouy, Anthony   +5 more
core   +4 more sources

Adaptive meshless refinement schemes for RBF-PUM collocation

, 2018
In this paper we present an adaptive discretization technique for solving elliptic partial differential equations via a collocation radial basis function partition of unity method. In particular, we propose a new adaptive scheme based on the construction
Cavoretto, R., De Rossi, A.
core   +1 more source

PLANE WAVE STABILITY OF THE SPLIT-STEP FOURIER METHOD FOR THE NONLINEAR SCHRÖDINGER EQUATION

Forum of Mathematics, Sigma, 2014
Plane wave solutions to the cubic nonlinear Schrödinger equation on a torus have recently been shown to behave orbitally stable. Under generic perturbations of the initial data that are small in a high-order Sobolev norm, plane waves are stable over long
ERWAN FAOU, LUDWIG GAUCKLER, CHRISTIAN LUBICH   +2 more
doaj   +1 more source

New, Highly Accurate Propagator for the Linear and Nonlinear Schr\"odinger Equation

, 2012
A propagation method for the time dependent Schr\"odinger equation was studied leading to a general scheme of solving ode type equations. Standard space discretization of time-dependent pde's usually results in system of ode's of the form u_t -Gu = s ...
A. Alvermanna, C. Leforestier, D. Kosloff, D.J. Tannor, H. Tal Ezer, H. Tal Ezer, H. Tal Ezer, H.-D. Meyer, Hillel Tal-Ezer, Ido Schaefer, J.P. Palao, M. Caliari, M. Hochbruck, M. Hochbruck, M. Hochbruck, M. Ndong, M. Ndong, M.D. Feit, N.J. Higham, Ronnie Kosloff, U. Peskin   +20 more
core   +1 more source

Global regularity criterion for the 3D Navier-Stokes equations involving one entry of the velocity gradient tensor

, 2010
In this paper we provide a sufficient condition, in terms of only one of the nine entries of the gradient tensor, i.e., the Jacobian matrix of the velocity vector field, for the global regularity of strong solutions to the three-dimensional Navier-Stokes
C. Cao, C. Doering, C. He, Chongsheng Cao, D. Chae, Edriss S. Titi, G. Prodi, G. Raugel, G. Seregin, G.P. Galdi, H. Fujita, H. Sohr, H. Sohr, H.B. Da Veiga, I. Kukavica, I. Kukavica, J. Leray, J. Serrin, J.L. Lions, L. Escauriaza, L.C. Berselli, L.C. Berselli, M. Pokorný, M. Pokorný, O.A. Ladyzhenskaya, P. Constantin, P. Constantin, P.G. Lemarié–Rieusset, P.L. Lions, R. Sohr, R.A. Adams, T. Kato, Y. Giga, Y. Giga, Y. Zhou, Y. Zhou   +35 more
core   +1 more source

A Computational Scheme Based on Fractional Basis Functions For Solving Fractional Bagley–Torvik Equation

Journal of Mathematics, Volume 2025, Issue 1, 2025.
This study aims to present a spectral collocation approach for treating fractional Bagley–Torvik equations using fractional basis functions. The Bagley–Torvik equation is critically important in a wide range of applied scientific and engineering disciplines. The fractional form of the Bagley–Torvik equations enables the modeling of complex systems with
Taghipour M., Aminikhah H., Chang Phang
wiley   +1 more source

The solution of the scalar wave equation in the exterior of a sphere

, 2013
We derive new, explicit representations for the solution to the scalar wave equation in the exterior of a sphere, subject to either Dirichlet or Robin boundary conditions.
Greengard, Leslie, Hagstrom, Thomas, Jiang, Shidong   +2 more
core   +1 more source

A new operational matrix based on Bernoulli polynomials [PDF]

, 2014
In this research, the Bernoulli polynomials are introduced. The properties of these polynomials are employed to construct the operational matrices of integration together with the derivative and product.
Kazem, S., Parand, K., Rad, J. A., Shaban, M.   +3 more
core  

Petrov-Galerkin method for small deflections in fourth-order beam equations in civil engineering

Nonlinear Engineering
This study explores the Petrov–Galerkin method’s application in solving a linear fourth-order ordinary beam equation of the form u″″+qu=fu^{\prime\prime} ^{\prime\prime} +qu=f.
Youssri Youssri Hassan, Atta Ahmed Gamal, Abu Waar Ziad Yousef, Moustafa Mohamed Orabi   +3 more
doaj   +1 more source