Numerical solution of nonlinear Hunter-Saxton equation, Benjamin-Bona Mahony equation, and Klein-Gordon equation using Hosoya polynomial method

Nirmala, AN; Kumbinarasaiah, S.

doi:10.1016/j.rico.2024.100388

Cited by 4 publications

(1 citation statement)

References 30 publications

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“…Graph polynomials are employed in several other disciplines, such as economics and traffic control. They are also valuable for developing efficient analytical and numerical techniques for solving mathematical models [26][27][28][29]. These uses highlight the adaptability and strength of graph polynomials in the resolution of challenging mathematical models.…”

Section: Introductionmentioning

confidence: 99%

A numerical investigation of a well-known nonlinear Newell-Whitehead-Segel equation using the rank polynomial of the star graph

Kumbinarasaiah,

Nirmala

2024

Phys. Scr.

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Mathematical models of pattern formation are indispensable tools in various fields, from developmental biology to ecology, providing insights into complex phenomena and contributing to our understanding of the natural world. These patterns have been extensively studied using reaction-diffusion and NewellWhiteheadSegel models. This article intended to find an approximate numerical solution to the NewellWhiteheadSegel equation. The appearance of stripe patterns in two-dimensional systems is explained in nonlinear systems using the NewellWhiteheadSegel equation. Based on the function basis of rank polynomials of star graphs and the well-posed operational matrices, the rank polynomial collocation method is constructed. The alleged rank polynomial collocation method created a system of nonlinear algebraic equations from the nonlinear NewellWhiteheadSegel equation. The nonlinear NewellWhiteheadSegel equation solution is approximated by solving the resulting system via Newton's Raphson method. Numerical instances are provided to illustrate the validity and effectiveness of the technique. Verification of accuracy is accomplished by calculating error norms. The obtained numerical results show a reasonable degree of consistency with the findings reported in the current literature. The scheme's primary benefit is the algorithm's ease of implementation.

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Section: Introductionmentioning

confidence: 99%

A numerical investigation of a well-known nonlinear Newell-Whitehead-Segel equation using the rank polynomial of the star graph

Kumbinarasaiah,

Nirmala

2024

Phys. Scr.

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Influence of heat source/sink on a rotating cone in a rotating nanofluid with magnetic field impact: Application of Hosoya polynomial‐based collocation method

Sharma,

Srilatha,

Prakash

et al. 2024

Z Angew Math Mech

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The present analysis considers the angular velocities of the free flow and the arbitrarily fluctuating cone over time, leading to an unsteady stream over a rotating cone in a rotating nanofluid. The effects of heat source/sink and magnetic field on an unsteady flow past a rotating cone in a rotating nanoliquid are considered in this examination. The dimensional governing equations are transformed into nondimensional ordinary differential equations (ODEs) using the similarity variables. The nonlinear system of ODEs has been solved using the Hosoya polynomial‐based collocation method (HPBCM), and the obtained values are compared with the numerical method Runge Kutta Fehlberg's fourth‐fifth order (RKF‐45) scheme. The effects of numerous factors on the momentum and thermal distributions are shown graphically. Results reveal that the ratio of the cone angular velocity to the free stream angular velocity increases the velocity profile but converse trend is seen for the thermal profile. The upsurge in the values of the magnetic parameter intensifies the velocity profile. The rise in the values of the heat source/sink parameter upsurges the thermal profile. As the unsteady parameter increases temperature profile declines.

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An intriguing numerical strategy for Zakharov–Kuznetsov equation through graph-theoretic polynomials

Nirmala,

Kumbinarasaiah

2024

Phys. Scr.

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This paper explores graph-theoretic polynomials to find the approximate solution of the (2+1)D Time-fractional Zakharov-Kuznetsov(TF-Z-K) equation. The Zakharov-Kuznetsov equations govern the behavior of nonlinear acoustic waves in the plasma of hot isothermal electrons and cold ions in the presence of a homogeneous magnetic field. Independence polynomials of the Ladder-Rung graph serve as the polynomial approximation for the suggested Independence Polynomial Collocation Method (IPCM). The Caputo fractional derivatives are adopted to determine the fractional derivatives in the TF-Z-K equation. The TF-Z-K equation is converted into a system of nonlinear algebraic equations using the collocation points in IPCM. The Newton-Raphson approach yields the solution of the suggested method by solving the resulting system. We’ve compared a few scenarios with the tangible outcomes to validate the procedure. Quantitative outcomes match the current findings and validate the exactness of IPCM compared t o the recent numerical and semi-analytical approaches in the literature.

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Numerical solution of nonlinear Hunter-Saxton equation, Benjamin-Bona Mahony equation, and Klein-Gordon equation using Hosoya polynomial method

Cited by 4 publications

References 30 publications

A numerical investigation of a well-known nonlinear Newell-Whitehead-Segel equation using the rank polynomial of the star graph

A numerical investigation of a well-known nonlinear Newell-Whitehead-Segel equation using the rank polynomial of the star graph

Influence of heat source/sink on a rotating cone in a rotating nanofluid with magnetic field impact: Application of Hosoya polynomial‐based collocation method

An intriguing numerical strategy for Zakharov–Kuznetsov equation through graph-theoretic polynomials

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