scholarly journals Numerical study of time dependent flow of immiscible Saffman dusty (fluid-particle suspension) and Eringen micropolar fluids in a duct with a modified cubic B-spline Differential Quadrature method

2022 ◽  
Vol 130 ◽  
pp. 105758
Author(s):  
Rajesh Kumar Chandrawat ◽  
Varun Joshi ◽  
O. Anwar Bég
Keyword(s):  
Numerical Study ◽  
Differential Quadrature Method ◽  
Differential Quadrature ◽  
Time Dependent ◽  
Particle Suspension ◽  
Quadrature Method ◽  
Micropolar Fluids ◽  
B Spline ◽  
Dependent Flow ◽  
Fluid Particle Suspension

A new perspective for the numerical solutions of the cmKdV equation via modified cubic B-spline differential quadrature method

2018 ◽  
Vol 29 (06) ◽  
pp. 1850043 ◽  
Author(s):  
Ali Başhan ◽  
N. Murat Yağmurlu ◽  
Yusuf Uçar ◽  
Alaattin Esen
Keyword(s):  
Solitary Wave ◽  
Solitary Waves ◽  
Numerical Solutions ◽  
Differential Quadrature Method ◽  
Differential Quadrature ◽  
Present Approach ◽  
Test Problems ◽  
Quadrature Method ◽  
Error Norm ◽  
B Spline

In the present paper, a novel perspective fundamentally focused on the differential quadrature method using modified cubic B-spline basis functions are going to be applied for obtaining the numerical solutions of the complex modified Korteweg–de Vries (cmKdV) equation. In order to test the effectiveness and efficiency of the present approach, three test problems, that is single solitary wave, interaction of two solitary waves and interaction of three solitary waves will be handled. Furthermore, the maximum error norm [Formula: see text] will be calculated for single solitary wave solutions to measure the efficiency and the accuracy of the present approach. Meanwhile, the three lowest conservation quantities will be calculated and also used to test the efficiency of the method. In addition to these test tools, relative changes of the invariants will be calculated and presented. In the end of these processes, those newly obtained numerical results will be compared with those of some of the published papers. As a conclusion, it can be said that the present approach is an effective and efficient one for solving the cmKdV equation and can also be used for numerical solutions of other problems.

A Quintic B-Spline Based Differential Quadrature Method for Numerical Solution of Kuramoto-Sivashinsky Equation

2017 ◽  
Vol 18 (2) ◽  
pp. 103-114 ◽  
Author(s):  
R. C. Mittal ◽  
Sumita Dahiya
Keyword(s):  
Differential Quadrature Method ◽  
Coefficient Matrix ◽  
Differential Quadrature ◽  
Test Problems ◽  
Quadrature Method ◽  
Thomas Algorithm ◽  
B Spline ◽  
Algorithm Stability ◽  
Weighting Coefficients ◽  
Sivashinsky Equation

AbstractIn this paper, the Kuramoto-Sivashinsky equation is solved numerically by implementing a new differential quadrature technique that uses quintic B-spline as the basis functions for space integration. The derivatives are approximated using differential quadrature method. The weighting coefficients are obtained by semi-explicit algorithm including an algebraic system with penta-diagonal coefficient matrix that is solved using the five-band Thomas algorithm. Stability analysis of method has also been done. The accuracy of the proposed scheme is demonstrated by applying on five test problems. Some theoretical properties of KS equation like periodicity, monotonicity and dissipativity etc. have also been discussed. The results are also shown graphically to demonstrate the accuracy and capabilities of this method and comparative study is done with results available in literature. The computed results are found to be in good agreement with the analytical solutions.

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