Generalized Hermite Function Spectral-Collocation Method for KdV Equations

2019 ◽  
Vol 08 (04) ◽  
pp. 631-637
Author(s):  
冰冰 李
Keyword(s):  
Collocation Method ◽  
Spectral Collocation Method ◽  
Hermite Function ◽  
Spectral Collocation ◽  
Kdv Equations

A conservative spectral method for the coupled Schrödinger-KdV equations

2020 ◽  
Vol 31 (05) ◽  
pp. 2050074
Author(s):  
Hao Zhou ◽  
Danfu Han ◽  
Miaoyong Du ◽  
Yao Shi
Keyword(s):  
Time Dependence ◽  
Spectral Method ◽  
Collocation Method ◽  
Spectral Collocation Method ◽  
Spectral Collocation ◽  
Exponential Time ◽  
Exponential Time Differencing ◽  
Conservative Method ◽  
Kdv Equations ◽  
Implicit Schemes

In this work, we present a conservative method to solve the coupled Schrödinger-KdV (CSK) equations. The CSK equations are discretized in space by Fourier spectral collocation method and exponential time differencing with three-layer implicit schemes for time dependence. The scheme is decoupled and conserve semi-discrete three invariants. To demonstrate the accuracy and reliability of the used scheme, we use three invariants, [Formula: see text] and [Formula: see text] error norms. Numerical results manifest better performance of the scheme compared with other numerical schemes.

A multivariate spectral quasi-linearization method for the solution of (2+1) dimensional Burgers’ equations

2020 ◽  
Vol 21 (7-8) ◽  
pp. 683-691
Author(s):  
Phumlani G. Dlamini ◽  
Vusi M. Magagula
Keyword(s):  
Collocation Method ◽  
Three Dimensional ◽  
Linearization Method ◽  
High Accuracy ◽  
Time Variable ◽  
Spectral Collocation Method ◽  
Spectral Collocation ◽  
Burgers Equations ◽  
Grid Points ◽  
Linearization Techniques

AbstractIn this paper, we introduce the multi-variate spectral quasi-linearization method which is an extension of the previously reported bivariate spectral quasi-linearization method. The method is a combination of quasi-linearization techniques and the spectral collocation method to solve three-dimensional partial differential equations. We test its applicability on the (2 + 1) dimensional Burgers’ equations. We apply the spectral collocation method to discretize both space variables as well as the time variable. This results in high accuracy in both space and time. Numerical results are compared with known exact solutions as well as results from other papers to confirm the accuracy and efficiency of the method. The results show that the method produces highly accurate solutions and is very efficient for (2 + 1) dimensional PDEs. The efficiency is due to the fact that only few grid points are required to archive high accuracy. The results are portrayed in tables and graphs.

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