scholarly journals A simple finite-difference scheme for handling topography with the first-order wave equation

2017 ◽  
Vol 210 (1) ◽  
pp. 482-499 ◽  
Author(s):  
W.A. Mulder ◽  
M.J. Huiskes
Keyword(s):  
Wave Equation ◽  
Finite Difference ◽  
Difference Scheme ◽  
Finite Difference Scheme ◽  
First Order

scholarly journals ONE-STEP EXTRAPOLATION METHOD USING CHEBYSHEV’S RECURRENCE RELATION APPLIED TO SEISMIC MODELING

2016 ◽  
Vol 34 (4) ◽  
Author(s):  
Laura Lara Ortiz ◽  
Reynam C. Pestana
Keyword(s):  
Wave Equation ◽  
Finite Difference ◽  
Acoustic Wave ◽  
Difference Scheme ◽  
Chebyshev Polynomials ◽  
Finite Difference Scheme ◽  
Acoustic Wave Equation ◽  
Seismic Modeling ◽  
First Order ◽  
One Step

ABSTRACT. In this work we show that the solution of the first order differential wave equation for an analytical wavefield, using a finite-difference scheme in time, follows exactly the same recursion of modified Chebyshev polynomials. Based on this, we proposed a numerical...Keywords: seismic modeling, acoustic wave equation, analytical wavefield, Chebyshev polinomials. RESUMO. Neste trabalho, mostra-se que a solução da equação de onda de primeira ordem com um campo de onda analítico usando um esquema de diferenças finitas no tempo segue exatamente a relação de recorrência dos polinômios modificados de Chebyshev. O algoritmo...Palavras-chave: modelagem sísmica, equação da onda acústica, campo analítico, polinômios de Chebyshev.

A new staggered grid finite difference scheme optimised in the space domain for the first order acoustic wave equation

2018 ◽  
Vol 49 (6) ◽  
pp. 898-905 ◽  
Author(s):  
Wenquan Liang ◽  
Xiu Wu ◽  
Yanfei Wang ◽  
Jingjie Cao ◽  
Chaofan Wu ◽  
...  
Keyword(s):  
Wave Equation ◽  
Finite Difference ◽  
Acoustic Wave ◽  
Difference Scheme ◽  
Finite Difference Scheme ◽  
Staggered Grid ◽  
Acoustic Wave Equation ◽  
Space Domain ◽  
First Order

scholarly journals A finite difference scheme for a fluid dynamic traffic flow model appended with two-point boundary condition

2012 ◽  
Vol 31 ◽  
pp. 43-52 ◽  
Author(s):  
MO Gani ◽  
MM Hossain ◽  
LS Andallah
Keyword(s):  
Boundary Condition ◽  
Finite Difference ◽  
Difference Scheme ◽  
Traffic Flow ◽  
Finite Difference Scheme ◽  
Flow Model ◽  
Fluid Dynamic ◽  
Point Boundary ◽  
Traffic Flow Model ◽  
First Order

A fluid dynamic traffic flow model with a linear velocity-density closure relation is considered. The model reads as a quasi-linear first order hyperbolic partial differential equation (PDE) and in order to incorporate initial and boundary data the PDE is treated as an initial boundary value problem (IBVP). The derivation of a first order explicit finite difference scheme of the IBVP for two-point boundary condition is presented which is analogous to the well known Lax-Friedrichs scheme. The Lax-Friedrichs scheme for our model is not straight-forward to implement and one needs to employ a simultaneous physical constraint and stability condition. Therefore, a mathematical analysis is presented in order to establish the physical constraint and stability condition of the scheme. The finite difference scheme is implemented and the graphical presentation of numerical features of error estimation and rate of convergence is produced. Numerical simulation results verify some well understood qualitative behavior of traffic flow.DOI: http://dx.doi.org/10.3329/ganit.v31i0.10307GANIT J. Bangladesh Math. Soc. (ISSN 1606-3694) 31 (2011) 43-52

scholarly journals The integration of a biharmonic equation by an implicit scheme

2018 ◽  
Vol 80 (2) ◽  
pp. 114-118
Author(s):  
M. I. Popov
Keyword(s):  
Finite Difference ◽  
Boundary Conditions ◽  
Difference Scheme ◽  
Finite Difference Scheme ◽  
Biharmonic Equation ◽  
Point Pattern ◽  
Calculation Time ◽  
Partial Derivatives ◽  
First Order ◽  
Approximate Analytical Solutions

The paper presents a step-by-step construction of a finite-difference scheme for a heterogeneous biharmonic equation under zero boundary conditions superimposed on the desired function and its first-order partial derivatives. The finite-difference scheme is based on a square twenty-five-point pattern and has an implicit character. On analytical grid, the error of approximation of the biharmonic operator by the difference analog and the error of approximation of boundary conditions imposed on the first order partial derivatives are calculated by the expansion of the function in the Taylor series with the remainder term in the form of a Lagrange. The boundary conditions imposed on the sought function are satisfied precisely. A finite-difference scheme approximates a boundary value problem with a second order of accuracy over the mesh step. With the help of the Maple computer algebra system the solutions of the problem for different grid steps are obtained. The dependence of the minimum function and calculation time on the number of significant digits is revealed. The optimal number of significant digits is found. The convergence rate of the numerical scheme is analyzed. The dependence of the minimum value of the function and the calculation time on the value of the grid step is established. The optimal step value is found. A three-dimensional graph of the solution and its profiles in the middle sections are constructed. The advantages of the developed finite-difference scheme are indicated. Obtained results correspond to the physical meaning of the problem and are consistent with similar numerical and approximate analytical solutions.

Sign in / Sign up

Export Citation Format

Share Document