Stability and error analysis for a second-order approximation of 1D nonlocal Schrödinger equation under DtN-type boundary conditions

2021 ◽  
Author(s):  
Jihong Wang ◽  
Jiwei Zhang ◽  
Chunxiong Zheng
Keyword(s):  
Schrödinger Equation ◽  
Error Analysis ◽  
Boundary Conditions ◽  
Schrodinger Equation ◽  
Order Approximation ◽  
Second Order ◽  
Second Order Approximation ◽  
Type Boundary ◽  
Stability And Error Analysis

scholarly journals Beyond periodic revivals for linear dispersive PDEs

2021 ◽  
Vol 477 (2251) ◽  
pp. 20210241
Author(s):  
Lyonell Boulton ◽  
George Farmakis ◽  
Beatrice Pelloni
Keyword(s):  
Schrödinger Equation ◽  
Boundary Conditions ◽  
Schrodinger Equation ◽  
Finite Interval ◽  
Periodic Boundary Conditions ◽  
Periodic Case ◽  
Initial Condition ◽  
Not Given ◽  
Airy Equation ◽  
Type Boundary

We study the phenomenon of revivals for the linear Schrödinger and Airy equations over a finite interval, by considering several types of non-periodic boundary conditions. In contrast to the case of the linear Schrödinger equation examined recently (which we develop further), we prove that, remarkably, the Airy equation does not generally exhibit revivals even for boundary conditions very close to periodic. We also describe a new, weaker form of revival phenomena, present in the case of certain Robin-type boundary conditions for the linear Schrödinger equation. In this weak revival, the dichotomy between the behaviour of the solution at rational and irrational times persists, but in contrast to the classical periodic case, the solution is not given by a finite superposition of copies of the initial condition.

Second order approximation of wave-structure couplings

1995 ◽  
Vol 22 (1) ◽  
pp. 49-64
Author(s):  
E.T. Huang ◽  
Yuh-Lin Hwang
Keyword(s):  
Order Approximation ◽  
Wave Structure ◽  
Second Order ◽  
Second Order Approximation
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