Numerical Solution of Generalized Kuramoto–Sivashinsky Equation Using Cubic Trigonometric B-Spline Based Differential Quadrature Method and One-Step Optimized Hybrid Block Method

2022 ◽  
Vol 8 (1) ◽  
Author(s):  
Anurag Kaur ◽  
V. Kanwar
Keyword(s):  
Numerical Solution ◽  
Differential Quadrature Method ◽  
Differential Quadrature ◽  
Quadrature Method ◽  
Block Method ◽  
B Spline ◽  
One Step ◽  
Sivashinsky Equation

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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