A Comparison Study of HO-CFD and DSC-RSK with Small Computational Bandwidths for Solving Some Classes of Boundary-Value and Eigenvalue Problems

2019 ◽  
Vol 17 (06) ◽  
pp. 1950011 ◽  
Author(s):  
Wei Li ◽  
Zhiwei Song ◽  
Xiaoqiao He ◽  
De Xie
Keyword(s):  
Finite Difference ◽  
Eigenvalue Problems ◽  
Boundary Value ◽  
Comparison Study ◽  
Comparison Analysis ◽  
Small Bandwidth ◽  
Discrete Singular Convolution ◽  
Cfd Method ◽  
Central Finite Difference ◽  
New Strategies

This paper conducts a comparison analysis of high order central finite difference (HO-CFD) method and discrete singular convolution-regularized Shannon kernel (DSC-RSK) scheme with small computational bandwidths for solving some classes of boundary-value and eigenvalue problems. Second-, fourth- and sixth-order partial differential equations are taken into account. New strategies to generate parameters [Formula: see text] in DSC-RSK are proposed to ensure minimum errors for each case, and the influence of parameters [Formula: see text] with more decimal places is analyzed. Apart from the existing matched interface and boundary (MIB) scheme, a new double-parameter MIB scheme is also proposed. The influence of small computational bandwidths is discussed in detail. Numerical results by using HO-CFD and DSC-RSK are presented and compared to illustrate the performance of both methods in small bandwidth limit. Some remarkable conclusions have been drawn at the end of this study.

scholarly journals Two new finite difference methods for computing eigenvalues of a fourth order linear boundary value problem

1987 ◽  
Vol 10 (3) ◽  
pp. 525-529 ◽  
Author(s):  
Riaz A. Usmani ◽  
Manabu Sakai
Keyword(s):  
Finite Difference ◽  
Boundary Value Problem ◽  
Fourth Order ◽  
Eigenvalue Problems ◽  
Order Differential Equation ◽  
Boundary Value ◽  
Finite Difference Methods ◽  
Practical Usefulness ◽  
Difference Methods ◽  
Linear Boundary Value Problem

This paper describes some new finite difference methods of order2and4for computing eigenvalues of a two-point boundary value problem associated with a fourth order differential equation of the form(py″)′​′+(q−λr)y=0. Numerical results for two typical eigenvalue problems are tabulated to demonstrate practical usefulness of our methods.

Numerical methods for solving the first-kind boundary value problem for a linear second-order differential equation with a deviating argument

2017 ◽  
Vol 23 (2) ◽  
Author(s):  
Muhad H. Abregov ◽  
Vladimir Z. Kanchukoev ◽  
Maryana A. Shardanova
Keyword(s):  
Differential Equation ◽  
Numerical Methods ◽  
Finite Difference ◽  
Boundary Value Problem ◽  
Order Differential Equation ◽  
Boundary Value ◽  
Sufficient Conditions ◽  
Second Order ◽  
Deviating Argument ◽  
Second Order Differential Equation

AbstractThis work is devoted to the numerical methods for solving the first-kind boundary value problem for a linear second-order differential equation with a deviating argument in minor terms. The sufficient conditions of the one-valued solvability are established, and the a priori estimate of the solution is obtained. For the numerical solution, the problem studied is reduced to the equivalent boundary value problem for an ordinary linear differential equation of fourth order, for which the finite-difference scheme of second-order approximation was built. The convergence of this scheme to the exact solution is shown under certain conditions of the solvability of the initial problem. To solve the finite-difference problem, the method of five-point marching of schemes is used.

scholarly journals the numerical solution of two point boundary value problem for the Helmholtz type equation by finite difference method with non regular step length between nodes

2021 ◽  
Vol 1 (1) ◽  
pp. 18-23
Author(s):  
Pramod Pandey
Keyword(s):  
Finite Difference ◽  
Finite Difference Method ◽  
Numerical Solution ◽  
Difference Method ◽  
Boundary Value ◽  
Type Equation ◽  
Step Length ◽  
Computational Results ◽  
Order Of Accuracy ◽  
Variable Step

In this article, we have presented a variable step finite difference method for solving second order boundary value problems in ordinary differential equations. We have discussed the convergence and established that proposed has at least cubic order of accuracy. The proposed method tested on several model problems for the numerical solution. The numerical results obtained for these model problems with known / constructed exact solution confirm the theoretical conclusions of the proposed method. The computational results obtained for these model problems suggest that method is efficient and accurate.

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