scholarly journals An Unconventional Finite Difference Scheme for Modified Korteweg-de Vries Equation

2017 ◽  
Vol 2017 ◽  
pp. 1-9 ◽  
Author(s):  
Canan Koroglu ◽  
Ayhan Aydin
Keyword(s):  
Finite Difference ◽  
Difference Scheme ◽  
Finite Difference Scheme ◽  
Truncation Error ◽  
Vries Equation ◽  
Mkdv Equation ◽  
Numerical Results ◽  
De Vries ◽  
Nsfd Scheme ◽  
Theta Method

A numerical solution of the modified Korteweg-de Vries (MKdV) equation is presented by using a nonstandard finite difference (NSFD) scheme with theta method which includes the implicit Euler and a Crank-Nicolson type discretization. Local truncation error of the NSFD scheme and linear stability analysis are discussed. To test the accuracy and efficiency of the method, some numerical examples are given. The numerical results of NSFD scheme are compared with the exact solution and a standard finite difference scheme. The numerical results illustrate that the NSFD scheme is a robust numerical tool for the numerical integration of the MKdV equation.

scholarly journals A Non-Standard Finite Difference Scheme for Magneto-Hydro Dynamics Boundary Layer Flows of an Incompressible Fluid Past a Flat Plate

2021 ◽  
Vol 26 (1) ◽  
pp. 22
Author(s):  
Riccardo Fazio ◽  
Alessandra Jannelli
Keyword(s):  
Boundary Layer ◽  
Finite Difference ◽  
Incompressible Fluid ◽  
Difference Scheme ◽  
Flat Plate ◽  
Finite Difference Scheme ◽  
Approximate Solutions ◽  
Numerical Results ◽  
Uniform Mesh ◽  
Wide Range

This paper deals with a non-standard implicit finite difference scheme that is defined on a quasi-uniform mesh for approximate solutions of the Magneto-Hydro Dynamics (MHD) boundary layer flow of an incompressible fluid past a flat plate for a wide range of the magnetic parameter. The proposed approach allows imposing the given boundary conditions at infinity exactly. We show how to improve the obtained numerical results via a mesh refinement and a Richardson extrapolation. The obtained numerical results are favourably compared with those available in the literature.

The Vibrations of an Infinite Orthotropic Layered Cylindrical Viscoelastic Shell in an Acoustic Medium

1976 ◽  
Vol 43 (4) ◽  
pp. 668-670 ◽  
Author(s):  
B. S. Berger
Keyword(s):  
Finite Difference ◽  
Difference Scheme ◽  
Numerical Solution ◽  
Finite Difference Scheme ◽  
Elastic Shell ◽  
Numerical Results ◽  
Acoustic Medium ◽  
Viscoelastic Shell ◽  
Cylindrical Viscoelastic Shell ◽  
Acoustic Fluid

In the following a numerical solution is given for the vibration of an orthotropic layered cylindrical viscoelastic shell in an acoustic medium. The acoustic fluid is modeled through a finite-difference scheme. Numerical results for the elastic shell in an acoustic medium agree with previous solutions.

scholarly journals DIFFERENCE SCHEME FOR DYNAMIC SIMULATION DESCRIBING STOCHASTIC KINETICS OF MOLECULES IN CERAMICS

1998 ◽  
Vol 3 (1) ◽  
pp. 93-97
Author(s):  
V. Frishfelds ◽  
I. Madzhulis ◽  
J. Rimshans
Keyword(s):  
Finite Difference ◽  
Difference Scheme ◽  
Dynamic Simulation ◽  
Finite Difference Scheme ◽  
Numerical Results ◽  
Computational Experiments ◽  
Kinetics Of ◽  
Stochastic Kinetics

A conservative and monotonous finite difference scheme is proposed for solving PDE describing the kinetics of molecules in ceramics. Numerical results of computational experiments are presented.

NUMERICAL STUDY OF THE WAVE INSTABILITY PROBLEM WITH THE EFFECT OF THE TRANSVERSE VELOCITY COMPONENT TEX SYSTEM

2001 ◽  
Vol 09 (03) ◽  
pp. 1055-1065
Author(s):  
B. S. ATTILI
Keyword(s):  
Finite Difference ◽  
Difference Scheme ◽  
Velocity Component ◽  
Finite Difference Scheme ◽  
Numerical Study ◽  
Transverse Velocity ◽  
Numerical Results ◽  
Wave Instability ◽  
Transverse Velocity Component ◽  
Instability Problem

We will numerically investigate the wave instability problem with the effect of the transverse velocity component. An accurate and easy to program finite difference scheme will be developed for this purpose. The eigenfunctions will be normalized and computed simultaneously with the eigenvectors. Numerical results will also be presented.

scholarly journals Explicit Exponential Finite Difference Scheme for 1D Navier-Stokes Equation with Time Dependent Pressure Gradient

2017 ◽  
Vol 36 ◽  
pp. 79-90
Author(s):  
MAK Azad ◽  
LS Andallah
Keyword(s):  
Finite Difference ◽  
Difference Scheme ◽  
Stokes Equation ◽  
Finite Difference Scheme ◽  
Burgers Equation ◽  
Numerical Technique ◽  
Numerical Results ◽  
Time Dependent ◽  
Navier Stokes ◽  
Navier Stokes Equation

In this paper, numerical technique for solving the one-dimensional (1D) unsteady, incompressible Navier-Stokes equation (NSE) is presented. The governing time dependent non-linear partial equation is reduced to non-linear partial differential equation named as viscous Burgers’ equation by introducing Orlowski and Sobczyk transformation (OST). An explicit exponential finite difference scheme (Expo FDS) has been used for solving reduced 1D NSE. The accuracy of the method has been illustrated by taking two numerical examples. Results are compared with the analytical solutions and those obtained based on the numerical results of reduced 1D NSE as Burgers’ equation. The accuracy and numerical feature of convergence of the Expo FDS is presented by estimating their error norms. Excellent numerical results indicate that the proposed numerical technique is efficient admissible with efficient accuracy for the numerical solutions of the NSE.GANIT J. Bangladesh Math. Soc.Vol. 36 (2016) 79-90

scholarly journals A Non-Standard Finite Difference Scheme for Magneto-Hydro Dynamics Boundary Layer Flows of an Incompressible Fluid Past a Flat Plate

2021 ◽  
Author(s):  
Riccardo Fazio ◽  
Alessandra Jannelli
Keyword(s):  
Boundary Layer ◽  
Finite Difference ◽  
Incompressible Fluid ◽  
Difference Scheme ◽  
Flat Plate ◽  
Finite Difference Scheme ◽  
Approximate Solutions ◽  
Numerical Results ◽  
Uniform Mesh ◽  
Wide Range

This paper deals with a non-standard finite difference scheme defined on a quasi-uniform mesh for approximate solutions of the Magneto-Hydro Dynamics (MHD) boundary layer flow of an incompressible fluid past a flat plate for a wide range of the magnetic parameter. We show how to improve the obtained numerical results via a mesh refinement and a Richardson extrapolation. The obtained numerical results are favourably compared with those available in the literature.

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