Results 31 to 40 of about 3,690 (92)

Parallelization of Faber Polynomial Based Propagators for Laser Applications

International Journal of Numerical Modelling: Electronic Networks, Devices and Fields, Volume 38, Issue 4, July/August 2025.
ABSTRACT In order to simulate a laser system, the evaluation of a complex semilinear master equation is needed, including the description of the wave propagation by Maxwell's equations and appropriate rate equations. The denser the spatial discretization, the slower the computation time of the time‐dependent propagator.
Wladimir Plotnikov, Dirk Schulz
wiley   +1 more source

Some symmetry classifications of hyperbolic vector evolution equations

, 2005
Motivated by recent work on integrable flows of curves and 1+1 dimensional sigma models, several O(N)-invariant classes of hyperbolic equations $u_{tx} =f(u,u_t,u_x)$ for an $N$-component vector $u(t,x)$ are considered.
Habibullin I T, Sanders J A, Sharpe R W, Sokolov V V   +3 more
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On the set of initial guesses for the secant method

Mathematical Methods in the Applied Sciences, Volume 48, Issue 7, Page 7398-7411, 15 May 2025.
The secant method is the most used iterative method to solve an operator equation where the operator involved is nondifferentiable. A known problem that arises when applying this method is its accessibility. Then, we try to improve it by using the technique of decomposition of the operator involved, so that the operator is in turn the sum of two ...
Alejandro Moysi, José Antonio Ezquerro, Miguel Ángel Hernández‐Verón, Ángel Alberto Magreñán   +3 more
wiley   +1 more source

Enhanced Group Analysis and Exact Solutions of Variable Coefficient Semilinear Diffusion Equations with a Power Source

, 2008
A new approach to group classification problems and more general investigations on transformational properties of classes of differential equations is proposed.
A.A. Abramenko, A.D. Polyanin, A.G. Nikitin, C. Sophocleous, D.J. Arrigo, D.J. Arrigo, E.T. Whittaker, F. Cariello, G.W. Bluman, G.W. Bluman, I.Sh. Akhatov, J. Crank, J. Patera, J.D. Murray, J.G. Kingston, J.G. Kingston, J.G. Kingston, L. Gagnon, L.A. Peletier, L.V. Ovsiannikov, L.V. Ovsiannikov, M.J. Ablowitz, M.L. Gandarias, N.I. Serov, N.M. Ivanova, O. O. Vaneeva, O.O. Vaneeva, P. Basarab-Horwath, P. Olver, P.A. Clarkson, R. Cherniha, R. Cherniha, R. O. Popovych, R.O. Popovych, R.O. Popovych, R.Z. Zhdanov, R.Z. Zhdanov, R.Z. Zhdanov, R.Z. Zhdanov, S. Kamin, S. Lie, S. Lie, S.V. Meleshko, V. Lahno, V.A. Dorodnitsyn, V.I. Lagno, V.I. Lahno, W. Hereman, W.I. Fushchich, W.I. Fushchych, W.I. Fushchych, W.I. Fushchych, X.Y. Wang, Y.S. Touloukian   +53 more
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Forward uncertainty quantification in random differential equation systems with delta‐impulsive terms: Theoretical study and applications

Mathematical Methods in the Applied Sciences, Volume 48, Issue 7, Page 7609-7629, 15 May 2025.
This contribution aims at studying a general class of random differential equations with Dirac‐delta impulse terms at a finite number of time instants. Our approach directly addresses calculating the so‐called first probability density function, from which all the relevant statistical information about the solution, a stochastic process, can be ...
Vicente J. Bevia, Juan C. Cortés, Rafael J. Villanueva   +2 more
wiley   +1 more source

Lie point symmetries and ODEs passing the Painlev\'e test

, 2018
The Lie point symmetries of ordinary differential equations (ODEs) that are candidates for having the Painlev\'e property are explored for ODEs of order $n =2, \dots ,5$. Among the 6 ODEs identifying the Painlev\'e transcendents only $P_{III}$, $P_V$ and
Levi, Decio, Sekera, David, Winternitz, Pavel   +2 more
core   +1 more source

The free boundary for semilinear problems with highly oscillating singular terms

Journal of the London Mathematical Society, Volume 111, Issue 5, May 2025.
Abstract We investigate general semilinear (obstacle‐like) problems of the form Δu=f(u)$\Delta u = f(u)$, where f(u)$f(u)$ has a singularity/jump at {u=0}$\lbrace u=0\rbrace$ giving rise to a free boundary. Unlike many works on such equations where f$f$ is approximately homogeneous near {u=0}$\lbrace u = 0\rbrace$, we work under assumptions allowing ...
Mark Allen, Dennis Kriventsov, Henrik Shahgholian   +2 more
wiley   +1 more source

A non-injective version of Wigner's theorem

, 2018
Let $H$ be a complex Hilbert space and let ${\mathcal F}_{s}(H)$ be the real vector space formed by all self-adjoint finite rank operators on $H$. We prove the following non-injective version of Wigner's theorem: every linear operator on ${\mathcal F}_{s}
Pankov, Mark, Plevnik, Lucijan
core  

Arithmetic Satake compactifications and algebraic Drinfeld modular forms

Journal of the London Mathematical Society, Volume 111, Issue 4, April 2025.
Abstract In this article, we construct the arithmetic Satake compactification of the Drinfeld moduli schemes of arbitrary rank over the ring of integers of any global function field away from the level structure, and show that the universal family extends uniquely to a generalized Drinfeld module over the compactification.
Urs Hartl, Chia‐Fu Yu
wiley   +1 more source

Some forms of exceptional Lie algebras [PDF]

, 2013
Some forms of Lie algebras of types E_6, E_7, and E_8 are constructed using the exterior cube of a rank 9 finitely generated projective ...
Faulkner, John R.
core