A Hybrid Finite-Volume/Finite-Difference Scheme for One-Dimensional Boussinesq Equations to Simulate Wave Attenuation Due to Vegetation

2011 ◽  
Author(s):  
S. N. Kuiry ◽  
W. Wu ◽  
Y. Ding
Keyword(s):  
Finite Difference ◽  
Difference Scheme ◽  
Finite Volume ◽  
Finite Difference Scheme ◽  
Wave Attenuation ◽  
Boussinesq Equations ◽  
One Dimensional

scholarly journals Convergence of a finite difference scheme for von Foerster equation with functional dependence

2012 ◽  
Vol 45 (3) ◽  
Author(s):  
Piotr Zwierkowski
Keyword(s):  
Finite Difference ◽  
Difference Scheme ◽  
Finite Difference Scheme ◽  
Functional Dependence ◽  
Spatial Variable ◽  
One Dimensional ◽  
Numerical Example

AbstractWe analyse a finite difference scheme for von Foerster–McKendrick type equations with functional dependence forward in time and backward with respect to one dimensional spatial variable. Some properties of solutions of a scheme are given. Convergence of a finite difference scheme is proved. The presented theory is illustrated by a numerical example.

scholarly journals A Multilevel Finite Difference Scheme for One-Dimensional Burgers Equation Derived from the Lattice Boltzmann Method

2012 ◽  
Vol 2012 ◽  
pp. 1-13 ◽  
Author(s):  
Qiaojie Li ◽  
Zhoushun Zheng ◽  
Shuang Wang ◽  
Jiankang Liu
Keyword(s):  
Finite Difference ◽  
Difference Scheme ◽  
Lattice Boltzmann Method ◽  
Lattice Boltzmann ◽  
Finite Difference Scheme ◽  
Numerical Solutions ◽  
Burgers Equation ◽  
One Dimensional ◽  
Explicit Finite Difference ◽  
Boltzmann Method

An explicit finite difference scheme for one-dimensional Burgers equation is derived from the lattice Boltzmann method. The system of the lattice Boltzmann equations for the distribution of the fictitious particles is rewritten as a three-level finite difference equation. The scheme is monotonic and satisfies maximum value principle; therefore, the stability is proved. Numerical solutions have been compared with the exact solutions reported in previous studies. TheL2, L∞and Root-Mean-Square (RMS) errors in the solutions show that the scheme is accurate and effective.

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