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The phase flow method
The phase flow method Ordinary differential equations Phase maps Phase flow Interpolation High-frequency wave propagation Geometrical optics Hamiltonian dynamics Ray equations Wave arrival times Eulerian and Lagrangian formulations
2015/7/14
This paper introduces the phase flow method, a novel, accurate and fast approach for constructing phase maps for nonlinear autonomous ordinary differential equations. The method operates by initially ...
The Phase Flow Method
The phase flow method ordinary differential equations phase maps phase flow interpolation high-frequency wave propagation geometrical optics Hamiltonian dynamics ray equations wave arrival times Eulerian and Lagrangian formulations
2015/6/17
This paper introduces the phase flow method, a novel, accurate and fast approach for constructing phase maps for nonlinear autonomous ordinary differential equations. The method operates by initially ...
A Differential Equation for Modeling Nesterov’s Accelerated Gradient Method:Theory and Insights
Differential Equation Modeling Nesterov’s Accelerated Gradient Method Theory Insights
2015/6/17
We derive a second-order ordinary differential equation (ODE), which is the limit of Nesterov’s accelerated gradient method. This ODE exhibits approximate equivalence to Nesterov’s scheme and thus can...
A Differential Equation for Modeling Nesterov’s Accelerated Gradient Method:Theory and Insights
Nesterov’s accelerated scheme convex optimization first-order methods differential equation restarting
2015/6/17
We derive a second-order ordinary differential equation (ODE) which is the limit of Nesterov’s accelerated gradient method. This ODE exhibits approximate equivalence to Nesterov’s scheme and thus can ...
A discontinuous Galerkin method for the Vlasov-Poisson system
Discontinuous Galerkin method Vlasov-Poisson system
2010/12/15
A discontinuous Galerkin method for approximating the Vlasov-Poisson system of equations describing the time evolution of a collisionless plasma is proposed. The method is mass conservative and, in th...
In this paper, we develop a new teclinique called multiplicative extrapolation method which is used to construct higher order schemes for ordinary dtherential equations. We call it a new method becaus...
Solving second order equations by extending the PS method
second order equations extending the PS method
2010/11/1
An extension of the ideas of the Prelle-Singer procedure to second order differential equations is proposed. As in the original PS procedure, this version of our method deals with differential equati...
Difference Method for a Singularly Perturbed Initial Value Problem
Initial Value Problem discrete maximum norm
2010/3/4
In this paper we construct a completely exponentially fitted finite difference scheme for the initial value problem with small parameter by first and second derivatives. We prove the first order unifo...