Optimal error estimate of a compact scheme for nonlinear Schrödinger equation

2017 ◽  
Vol 120 ◽  
pp. 68-81 ◽  
Author(s):  
Jialin Hong ◽  
Lihai Ji ◽  
Linghua Kong ◽  
Tingchun Wang
Keyword(s):  
Schrödinger Equation ◽  
Error Estimate ◽  
Nonlinear Schrödinger Equation ◽  
Schrodinger Equation ◽  
Nonlinear Schrodinger Equation ◽  
Compact Scheme ◽  
Optimal Error Estimate ◽  
Optimal Error ◽  
Nonlinear Schrödinger

Numerical Methods for the Derivative Nonlinear Schrödinger Equation

2018 ◽  
Vol 19 (3-4) ◽  
pp. 239-249 ◽  
Author(s):  
Shu-Cun Li ◽  
Xiang-Gui Li ◽  
Fang-Yuan Shi
Keyword(s):  
Schrödinger Equation ◽  
Nonlinear Schrödinger Equation ◽  
Schrodinger Equation ◽  
Nonlinear Schrodinger Equation ◽  
Second Order ◽  
Compact Scheme ◽  
Order Accuracy ◽  
Nonlinear Schrödinger ◽  
Accuracy Order ◽  
Derivative Nonlinear Schrödinger Equation

AbstractIn this work, a second-order accuracy in both space and time Crank–Nicolson (C-N)-type scheme, a fourth-order accuracy in space and second-order accuracy in time compact scheme and a sixth-order accuracy in space and second-order accuracy in time compact scheme are proposed for the derivative nonlinear Schrödinger equation. The C-N-type scheme is tested to satisfy the conservation of discrete mass. For the two compact schemes, the iterative algorithm and the Thomas algorithm in block matrix form are adopted to enhance the computational efficiency. Numerical experiment is given to test the mass conservation for the C-N-type scheme as well as the accuracy order of the three schemes. In addition, the numerical simulation of binary collision and the influence on the solitary solution by adding a small random perturbation to the initial condition are also discussed.

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