| Volume 15, Number 1, 2025, Pages - DOI：10.11948/JAAC-2023-0419 |
| A novel approach for the nonlinear elliptic partial differential equations using Clique polynomials of Graph |
| Kumbinarasaiah S,Hadi Rezazadeh,Hijaz Ahmad |
| Keywords:Nonlinear elliptic partial differential equations collocation technique Complete Graph Clique polynomials |
| Abstract: |
| This study proposed an efficient numerical technique for nonlinear elliptic partial
differential equations (EPDEs) using the functional matrix generated by Clique polynomials
of Complete Graph. Recently, Graph theory has attracted many mathematicians" attention
due to its wide applications. Here, Three nonlinear problems have been considered to
examine the proposed scheme proficiency. Some theorems on convergence are discussed.
Here, the nonlinear elliptic PDEs are rehabilitated into a nonlinear algebraic equation
system using the operational matrix of Clique polynomials and collocation technique. Using
the Newton-Raphson method, we numerically solved this system of algebraic equations to
the desired results. The proposed scheme results are compared with the literature"s analytical
and other method solutions through tables and graphs. Tables and graphs are used to support
the proposed technique"s efficacy and accuracy. The obtained results reveal that the current
approach is more accurate than other methods. The theorems are used to draw the
convergent analysis for the suggested approach.
From the obtained results, we can conclude that, in order to find a numerical solution for
these kinds of nonlinear EPDEs, the method is extremely effective, requires less
computational effort, and is easy to implement. |
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