A difference scheme for solving the initial value problem for one-dimensional Vlasov equations

1982 ◽  
Vol 22 (2) ◽  
pp. 174-180
Author(s):  
M.I. Letavin
Keyword(s):  
Difference Scheme ◽  
Initial Value Problem ◽  
Initial Value ◽  
One Dimensional ◽  
Vlasov Equations

scholarly journals Stability of Finite Difference Schemes on Irregular Meshes for Von Foerster-Type 1-D Equations

2007 ◽  
Vol 14 (4) ◽  
pp. 793-805
Author(s):  
Piotr Zwierkowski
Keyword(s):  
Finite Difference ◽  
Initial Value Problem ◽  
Difference Schemes ◽  
Spatial Variable ◽  
Finite Difference Schemes ◽  
Initial Value ◽  
One Dimensional ◽  
Irregular Meshes ◽  
The Stability

Abstract We consider a generalized von Foerster equation in one dimensional spatial variable and construct finite difference schemes for the initial value problem. The stability of finite difference schemes on irregular meshes generated by characteristics is studied.

scholarly journals Stability of a Second Order of Accuracy Difference Scheme for Hyperbolic Equation in a Hilbert Space

2007 ◽  
Vol 2007 ◽  
pp. 1-25 ◽  
Author(s):  
Allaberen Ashyralyev ◽  
Mehmet Emir Koksal
Keyword(s):  
Hilbert Space ◽  
Difference Scheme ◽  
Hyperbolic Equation ◽  
Initial Value Problem ◽  
Second Order ◽  
Stability Estimates ◽  
Initial Value ◽  
Order Of Accuracy ◽  
Positive Definite Operators ◽  
Accuracy Difference

The initial-value problem for hyperbolic equation d2u(t)/dt2+A(t)u(t)=f(t)(0≤t≤T), u(0)=ϕ,u′(0)=ψ in a Hilbert space H with the self-adjoint positive definite operators A(t) is considered. The second order of accuracy difference scheme for the approximately solving this initial-value problem is presented. The stability estimates for the solution of this difference scheme are established.

scholarly journals On the one dimensional cubic NLS in a critical space

2022 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Marco Bravin ◽  
Luis Vega
Keyword(s):  
Initial Data ◽  
Schrödinger Equation ◽  
Initial Value Problem ◽  
Schrodinger Equation ◽  
Three Dimensions ◽  
Critical Space ◽  
Initial Value ◽  
One Dimensional ◽  
Geometrical Problem ◽  
The One

<p style='text-indent:20px;'>In this note we study the initial value problem in a critical space for the one dimensional Schrödinger equation with a cubic non-linearity and under some smallness conditions. In particular the initial data is given by a sequence of Dirac deltas with different amplitudes but equispaced. This choice is motivated by a related geometrical problem; the one describing the flow of curves in three dimensions moving in the direction of the binormal with a velocity that is given by the curvature.</p>

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