A fourth-order difference scheme for quasilinear poisson equation in polar co-ordinates

1994 ◽  
Vol 10 (10) ◽  
pp. 791-797 ◽  
Author(s):  
M. K. Jain ◽  
R. K. Jain ◽  
Meera Krishna
Keyword(s):  
Difference Scheme ◽  
Poisson Equation ◽  
Fourth Order ◽  
Order Difference

scholarly journals Fourth-order finite difference scheme and efficient algorithm for nonlinear fractional Schrödinger equations

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Yan Chang ◽  
Huanzhen Chen
Keyword(s):  
Quantum Mechanics ◽  
Difference Scheme ◽  
Fourth Order ◽  
Convergence Rates ◽  
Order Convergence ◽  
Fractional Quantum ◽  
Order Difference ◽  
Computation Cost ◽  
Fractional Schrödinger Equations ◽  
Nonlinear Fractional Schrödinger Equations

AbstractTo improve the computing efficiency, a fourth-order difference scheme is proposed and a fast algorithm is designed to simulate the nonlinear fractional Schrödinger (FNLS) equation oriented from the fractional quantum mechanics. The numerical analysis and experiments conducted in this article show that the proposed difference scheme has the optimal second-order and fourth-order convergence rates in time and space respectively, reduces its computation cost to $\mathcal{O}(M\log M)$O(MlogM), and recognizes accurately its physical feature of FNLS such as the mass balance.

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