Concept

Trapezoidal rule (differential equations)

Related publications (9)

From low-rank retractions to dynamical low-rank approximation and back

Daniel Kressner, Axel Elie Joseph Séguin, Gianluca Ceruti

In algorithms for solving optimization problems constrained to a smooth manifold, retractions are a well-established tool to ensure that the iterates stay on the manifold. More recently, it has been demonstrated that retractions are a useful concept for ot ...

Springer2024

Time-reversible and norm-conserving high-order integrators for the nonlinear time-dependent Schrödinger equation: Application to local control theory

Jiri Vanicek, Julien Roulet

The explicit split-operator algorithm has been extensively used for solving not only linear but also nonlinear time-dependent Schrödinger equations. When applied to the nonlinear Gross–Pitaevskii equation, the method remains time-reversible, norm-conservin ...

2021

Efficient geometric integrators for nonadiabatic quantum dynamics. I. The adiabatic representation

Jiri Vanicek, Seonghoon Choi

Geometric integrators of the Schrödinger equation conserve exactly many invariants of the exact solution. Among these integrators, the split-operator algorithm is explicit and easy to implement but, unfortunately, is restricted to systems whose Hamiltonian ...

2019

Application of the Rosenbrock methods to the solution of unsteady 3D incompressible Navier-Stokes equations

Alfio Quarteroni, Michel Deville, Simone Deparis, Luca Pegolotti, Filippo Menghini

We consider the Rosenbrock methods, namely a family of methods for Differential Algebraic Equations, for the solution of the unsteady three-dimensional Navier-Stokes equations. These multistage schemes are attractive for non-linear problems because they ac ...

2018

High-Order Accurate Local Schemes for Fractional Differential Equations

Jan Sickmann Hesthaven, Daniel Henri Baffet

High-order methods inspired by the multi-step Adams methods are proposed for systems of fractional differential equations. The schemes are based on an expansion in a weighted space. To obtain the schemes this expansion is terminated after terms. We study t ...

Springer Verlag2017

High-Order Accurate Adaptive Kernel Compression Time-Stepping Schemes for Fractional Differential Equations

Jan Sickmann Hesthaven, Daniel Henri Baffet

High-order adaptive methods for fractional differential equations are proposed. The methods rely on a kernel reduction method for the approximation and localization of the history term. To avoid complications typical to multistep methods, we focus our stud ...

Springer Verlag2017

Methods of approximation influence aquatic ecosystem metabolism estimates

Janine Rüegg

Aquatic ecologists have recently employed dynamic models to estimate aquatic ecosystem metabolism. All approaches involve numerically solving a differential equation describing dissolved oxygen (DO) dynamics. Although the DO differential equation can be so ...

Association for the Sciences of Limnology and Oceanography2016

A method for the enumeration of the floppy modes and the calculation of the associated entropy

Giuseppe Foffi

We present a method that is based on the Ladd-Frenkel (LF) thermodynamic integration for the study of the rigidity of networks of particles bonded together by short-ranged square well attractive potentials. We show that, by taking the limit of the attracti ...

2008

Analytical solution of a convection-dispersion model with time-dependent transport coefficients

David Andrew Barry

Mathematical studies of solute transport in porous media have often utilized “equivalent” models of the transport process to remove undesired variability in the transport coefficients at the space and time scales of direct interest. Both deterministic and ...

1989

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