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Bibliographic Details
Main Authors:	Banks, J. W., Shatah, J.
Format:	Preprint
Published:	2025
Subjects:	Numerical Analysis
Online Access:	https://arxiv.org/abs/2509.03432
Tags:	Add Tag No Tags, Be the first to tag this record!

A Finite Difference Scheme for (2+1)D Cubic-Quintic Nonlinear Schrödinger Equations with Nonlinear Damping
by: Le, Anh Ha, et al.
Published: (2024)

High-order Accurate Implicit-Explicit Time-Stepping Schemes for Wave Equations on Overset Grids
by: Carson, Allison M., et al.
Published: (2024)

Continuation for Nonlinear Elliptic Partial Differential Equations Discretized by the Multiquadric Method
by: Fedoseyev, A. I., et al.
Published: (1998)

A Hyperbolic Approximation of the Nonlinear Schrödinger Equation
by: Biswas, Abhijit, et al.
Published: (2025)

A Directional-ODE Framework for Discretization of Advection-Diffusion Equations
by: Jafarimoghaddam, Amin, et al.
Published: (2025)

Numerical Schemes for 3-Wave Kinetic Equations: A Complete Treatment of the Collision Operator
by: Walton, Steven, et al.
Published: (2024)

A New Fast Direct Method For Solving Quasi-Toeplitz System of Equations
by: Hasanbeigi, Shahin
Published: (2024)

An Optimal O(N) Helmholtz Solver for Complex Geometry using WaveHoltz and Overset Grids
by: Appelo, Daniel, et al.
Published: (2025)

A Multi-Frequency Helmholtz Solver Based on the WaveHoltz Algorithm
by: Appelö, Daniel, et al.
Published: (2025)

Adaptive Finite Element Method for a Nonlinear Helmholtz Equation with High Wave Number
by: Jiang, Run, et al.
Published: (2024)

A Proximal Primal-Dual Approach to Generalized JKO Schemes for Doubly Nonlinear Parabolic Equations
by: Briceño-Arias, Luis M., et al.
Published: (2026)

A Schrödinger-Based Dispersive Regularization Approach for Numerical Simulation of One-Dimensional Shallow Water Equations
by: Fu, Guosheng, et al.
Published: (2026)

A Structurally Informed Data Assimilation Approach for Nonlinear Partial Differential Equations
by: Li, Tongtong, et al.
Published: (2023)

Long-time Integration of Nonlinear Wave Equations with Neural Operators
by: Lei, Guanhang, et al.
Published: (2024)

A Discrete-Time Random Feature Method for Nonlinear Evolution Equations with Implicit-Explicit Runge--Kutta Time Stepping
by: Zhou, Haoran, et al.
Published: (2026)

NonlinearSolve.jl: High-Performance and Robust Solvers for Systems of Nonlinear Equations in Julia
by: Pal, Avik, et al.
Published: (2024)

Discretization, Uniform-in-Time Estimations and Approximation of Invariant Measures for Nonlinear Stochastic Differential Equations with Non-Uniform Dissipativity
by: Huang, Shan, et al.
Published: (2025)

Adaptive Residual-Driven Newton Solver for Nonlinear Systems of Equations
by: Ding, Renjie, et al.
Published: (2025)

Explicit Local Time-Stepping for the Inhomogeneous Wave Equation with Optimal Convergence
by: Grote, Marcus J., et al.
Published: (2024)

Numerical Performance of Abs Codes for Nonlinear Systems of Equations
by: Bodon, E., et al.
Published: (2001)

Dynamical Tensor Train Approximation for Kinetic Equations
by: Wang, Geshuo, et al.
Published: (2025)

A Semi-Discrete Optimal Transport Scheme for the 3D Incompressible Semi-Geostrophic Equations
by: Lavier, Théo
Published: (2024)

Finite Element Convergence Analysis For Wave Equations With Time-Dependent Coefficients
by: Jarroudi, Oussama Al, et al.
Published: (2026)

Convexification for a Coefficient Inverse Problem for a System of Two Coupled Nonlinear Parabolic Equations
by: Klibanov, Michael V., et al.
Published: (2024)

Efficient Krylov-Regularization Solvers for Multiquadric RBF Discretizations of the 3D Helmholtz Equation
by: Guide, Mohamed El, et al.
Published: (2025)

A Galerkin Alternating Projection Method for Kinetic Equations in the Diffusive Limit
by: Ceruti, Gianluca, et al.
Published: (2025)

Solving Diffusion and Wave Equations Meshlessly via Helmholtz Equations
by: Johnson, Adam
Published: (2024)

A Gas-Kinetic Scheme for Maxwell Equations
by: Pu, Zhigang, et al.
Published: (2024)

Stochastic Optimal Prediction with Application to Averaged Euler Equations
by: Bell, John, et al.
Published: (2000)

Structure-Preserving Neural Ordinary Differential Equations for Stiff Systems
by: Loya, Allen Alvarez, et al.
Published: (2025)

Continuous Data Assimilation for the Navier-Stokes Equations with Nonlinear Slip Boundary Conditions
by: Wu, W. C., et al.
Published: (2025)

Neural Network Acceleration of Iterative Methods for Nonlinear Schrödinger Eigenvalue Problems
by: Peterseim, Daniel, et al.
Published: (2025)

Frozen Gaussian Grid-point Correction For Semi-classical Schrödinger Equation
by: Chai, Lihui, et al.
Published: (2025)

Large deviations principles for symplectic discretizations of stochastic linear Schrödinger Equation
by: Chen, Chuchu, et al.
Published: (2020)

A Mass Preserving Numerical Scheme for Kinetic Equations that Model Social Phenomena
by: Bahid, Yassin, et al.
Published: (2025)

Combining Hyperbolic Quadrature Method of Moments and Discrete-Velocity-Direction Models for Solving BGK-type Equations
by: Li, Tianshu, et al.
Published: (2024)

Rootfinding and Optimization Techniques for Solving Nonlinear Systems of Equations Arising from Cohesive Zone Models
by: Cattaneo, Alberto, et al.
Published: (2025)

Hermite Neural Network Simulation for Solving the 2D Schrodinger Equation
by: Parand, Kourosh, et al.
Published: (2024)

Monolithic Multigrid Preconditioners for High-Order Discretizations of Stokes Equations
by: Voronin, Alexey, et al.
Published: (2024)

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* * @return void */ public function writeClose() { // The assumption is that we're using PHP's ext/session. // session_write_close() will actually overwrite $_SESSION with an // empty array on completion -- which leads to a mismatch between what // is in the storage object and $_SESSION. To get around this, we // temporarily reset $_SESSION to an array, and then re-link it to // the storage object. // // Additionally, while you _can_ write to $_SESSION following a // session_write_close() operation, no changes made to it will be // flushed to the session handler. As such, we now mark the storage // object isImmutable. $storage = $this->getStorage(); if (! $storage->isImmutable()) { $_SESSION = $storage->toArray(true); session_write_close(); $storage->fromArray($_SESSION); $storage->markImmutable(); } } /** * Attempt to set the session name * * If the session has already been started, or if the name provided fails * validation, an exception will be raised. * * @param string $name * @return SessionManager * @throws Exception\InvalidArgumentException */ public function setName($name) { if ($this->sessionExists()) { throw new Exception\InvalidArgumentException( 'Cannot set session name after a session has already started'

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