High Accuracy Split-Step Finite Difference Method for Schrödinger-KdV Equations

2018 ◽  
Vol 70 (4) ◽  
pp. 413 ◽  
Author(s):  
Feng Liao ◽  
Lu-Ming Zhang
Keyword(s):  
Finite Difference ◽  
Finite Difference Method ◽  
Difference Method ◽  
High Accuracy ◽  
Kdv Equations

An Explicit Hermite-Taylor Method for the Schrödinger Equation

2017 ◽  
Vol 21 (5) ◽  
pp. 1207-1230 ◽  
Author(s):  
Daniel Appelö ◽  
Gunilla Kreiss ◽  
Siyang Wang
Keyword(s):  
Finite Difference ◽  
Finite Difference Method ◽  
Schrödinger Equation ◽  
Difference Method ◽  
Numerical Experiments ◽  
Schrodinger Equation ◽  
High Accuracy ◽  
Exponential Integrator ◽  
Taylor Method ◽  
Coarse Grids

AbstractAn explicit spectrally accurate order-adaptive Hermite-Taylor method for the Schrödinger equation is developed. Numerical experiments illustrating the properties of the method are presented. The method, which is able to use very coarse grids while still retaining high accuracy, compares favorably to an existing exponential integrator – high order summation-by-parts finite difference method.

scholarly journals A NUMERICAL SIMULATION OF MORPHOLOGICAL PROCESSES FOR A NAVIGATION CHANNEL

2007 ◽  
Vol 17 (1) ◽  
pp. 22-27
Author(s):  
Nguyen Van Diep ◽  
Dang Huu Chung
Keyword(s):  
Numerical Simulation ◽  
Finite Difference ◽  
Finite Difference Method ◽  
Difference Method ◽  
High Accuracy ◽  
Navigation Channel ◽  
Mathematical Equations ◽  
Morphological Processes ◽  
The Finite Difference Method ◽  
Interpolation Functions

The finite difference method was applied to simulate the morphological processes for a. navigation channel Mathematical equations were based on the SUTRENCH and PROFILE models proposed by L. C. van Rijn. The difficulties of treatment for bed boundary conditions were overcame flexibly by using the interpolation functions with high accuracy. The results obtained showed that the simulation is very suitable and able to be applied to practice problems.

scholarly journals Comparison of modified ADM and classical finite difference method for some third-order and fifth-order KdV equations

2021 ◽  
Vol 54 (1) ◽  
pp. 377-409
Author(s):  
Appanah Rao Appadu ◽  
Abey Sherif Kelil
Keyword(s):  
Exact Solution ◽  
Finite Difference ◽  
Finite Difference Method ◽  
Numerical Experiment ◽  
Difference Method ◽  
Numerical Experiments ◽  
Decomposition Method ◽  
Adomian Decomposition Method ◽  
Kdv Equations ◽  
Adomian Decomposition

Abstract The KdV equation, which appears as an asymptotic model in physical systems ranging from water waves to plasma physics, has been studied. In this paper, we are concerned with dispersive nonlinear KdV equations by using two reliable methods: Shehu Adomian decomposition method (STADM) and the classical finite difference method for solving three numerical experiments. STADM is constructed by combining Shehu’s transform and Adomian decomposition method, and the nonlinear terms can be easily handled using Adomian’s polynomials. The Shehu transform is used to accelerate the convergence of the solution series in most cases and to overcome the deficiency that is mainly caused by unsatisfied conditions in other analytical techniques. We compare the approximate and numerical results with the exact solution for the two numerical experiments. The third numerical experiment does not have an exact solution and we compare profiles from the two methods vs the space domain at some values of time. This study provides us with information about which of the two methods are effective based on the numerical experiment chosen. Knowledge acquired will enable us to construct methods for other related partial differential equations such as stochastic Korteweg-de Vries (KdV), KdV-Burgers, and fractional KdV equations.

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