| Volume 14, Number 4, 2024, Pages - DOI：10.11948/JAAC-2023-0114 |
| Numerical approach for the Hunter Saxton equation arising in liquid crystal model through Cocktail party graphs Clique polynomial |
| Kumbinarasaiah S,Nirmala A N |
| Keywords:Hunter Saxton Equation, Graph-theoretic polynomial called Clique polynomial, Cocktail party graph, Operational matrix, Convergence Analysis. |
| Abstract: |
| In this study, we extracted the Clique polynomials from the Cocktail party graph (CPG) and generated the generalized operational matrix of integration through the Clique polynomials of CPG. Then developed an effective computational technique called Cocktail party graphs Clique polynomial collocation method (CCCM) to obtain an approximate numerical solution for the nonlinear liquid crystal model called the Hunter-Saxton equation (HSE). The operational matrix of CPG has been used to reduce HSE into an algebraic system of nonlinear equations that makes the solution quite superficial. These nonlinear algebraic equations have been solved by the Newton Raphson method. This projected that CCCM is considerably efficacious on the computational ground for higher accuracy and convergence of numerical solutions. The solution of the HSE is presented through figures and tables for different values of and . The accuracy and efficiency of the proposed technique are analyzed based on absolute errors. We also provided the convergence and error analysis of our method and verified the results through two examples to confirm the accuracy of the theoretical results. |
PDF Download reader
|
|
|
|