scholarly journals A second order accuracy in time, Fourier pseudo-spectral numerical scheme for "Good" Boussinesq equation

2020 ◽  
Vol 25 (9) ◽  
pp. 3749-3768
Author(s):  
Zeyu Xia ◽  
◽  
Xiaofeng Yang ◽  
Keyword(s):  
Numerical Scheme ◽  
Boussinesq Equation ◽  
Second Order ◽  
Order Accuracy ◽  
Pseudo Spectral

scholarly journals Numerical Simulation for a Multidimensional Fourth-Order Nonlinear Fractional Subdiffusion Model with Time Delay

Mathematics ◽  
2021 ◽  
Vol 9 (23) ◽  
pp. 3050
Author(s):  
Sarita Nandal ◽  
Mahmoud A. Zaky ◽  
Rob H. De Staelen ◽  
Ahmed S. Hendy
Keyword(s):  
Fourth Order ◽  
Numerical Scheme ◽  
Source Term ◽  
Variable Coefficients ◽  
Second Order ◽  
Order Accuracy ◽  
Nonlinear Source ◽  
Second Order In Time ◽  
Convergence Orders ◽  
Temporal Direction

The purpose of this paper is to develop a numerical scheme for the two-dimensional fourth-order fractional subdiffusion equation with variable coefficients and delay. Using the L2−1σ approximation of the time Caputo derivative, a finite difference method with second-order accuracy in the temporal direction is achieved. The novelty of this paper is to introduce a numerical scheme for the problem under consideration with variable coefficients, nonlinear source term, and delay time constant. The numerical results show that the global convergence orders for spatial and time dimensions are approximately fourth order in space and second-order in time.

scholarly journals Numerical Analysis of Convection–Diffusion Using a Modified Upwind Approach in the Finite Volume Method

Mathematics ◽  
2020 ◽  
Vol 8 (11) ◽  
pp. 1869
Author(s):  
Arafat Hussain ◽  
Zhoushun Zheng ◽  
Eyaya Fekadie Anley
Keyword(s):  
Finite Volume Method ◽  
Finite Volume ◽  
Numerical Scheme ◽  
Diffusion Problem ◽  
Second Order ◽  
Order Accuracy ◽  
Central Difference ◽  
Convection Diffusion ◽  
Volume Method ◽  
And Diffusion

The main focus of this study was to develop a numerical scheme with new expressions for interface flux approximations based on the upwind approach in the finite volume method. Our new proposed numerical scheme is unconditionally stable with second-order accuracy in both space and time. The method is based on the second-order formulation for the temporal approximation, and an upwind approach of the finite volume method is used for spatial interface approximation. Some numerical experiments have been conducted to illustrate the performance of the new numerical scheme for a convection–diffusion problem. For the phenomena of convection dominance and diffusion dominance, we developed a comparative study of this new upwind finite volume method with an existing upwind form and central difference scheme of the finite volume method. The modified numerical scheme shows highly accurate results as compared to both numerical schemes.

A second order operator splitting numerical scheme for the “good” Boussinesq equation

2017 ◽  
Vol 119 ◽  
pp. 179-193 ◽  
Author(s):  
Cheng Zhang ◽  
Hui Wang ◽  
Jingfang Huang ◽  
Cheng Wang ◽  
Xingye Yue
Keyword(s):  
Numerical Scheme ◽  
Boussinesq Equation ◽  
Operator Splitting ◽  
Second Order ◽  
Order Operator

scholarly journals A pseudo-spectral Strang splitting method for linear dispersive problems with transparent boundary conditions

2021 ◽  
Author(s):  
L. Einkemmer ◽  
A. Ostermann ◽  
M. Residori
Keyword(s):  
Boundary Conditions ◽  
Splitting Method ◽  
Order Reduction ◽  
Second Order ◽  
Splitting Scheme ◽  
Transparent Boundary Conditions ◽  
Order Accuracy ◽  
Inflow Boundary Condition ◽  
Strang Splitting ◽  
Pseudo Spectral

AbstractThe present work proposes a second-order time splitting scheme for a linear dispersive equation with a variable advection coefficient subject to transparent boundary conditions. For its spatial discretization, a dual Petrov–Galerkin method is considered which gives spectral accuracy. The main difficulty in constructing a second-order splitting scheme in such a situation lies in the compatibility condition at the boundaries of the sub-problems. In particular, the presence of an inflow boundary condition in the advection part results in order reduction. To overcome this issue a modified Strang splitting scheme is introduced that retains second-order accuracy. For this numerical scheme a stability analysis is conducted. In addition, numerical results are shown to support the theoretical derivations.

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