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Journals / Turkish Journal of Mathematics / 2020 / Cilt: 44 - Sayı: 1

A reduced computational matrix approach with convergence estimation for solving model differential equations involving specific nonlinearities of quartic type

Ömür Kıvanç KÜRKÇÜ
Pages
223–239
Publication Date
2020-01-20
DOI
—
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AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

Numerical and graphical results are indicated to discuss the validity and efficiency of the method.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:This study aims to efficiently solve model differential equations involving specific nonlinearities of quartic type by proposing a reduced computational matrix approach based on the generalized Mott polynomial.
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Key Findings & Data:This method presents a reduced matrix expansion of the generalized Mott polynomial with the parameter-α, matrix equations, and Chebyshev--Lobatto collocation points.
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Conclusion & Impact:Numerical and graphical results are indicated to discuss the validity and efficiency of the method.
🔬Design:Modeling & Simulation
📍Scope:Comprehensive Sample
⚙️Variables:Matrix method · error estimation · Mott polynomial

Abstract

This study aims to efficiently solve model differential equations involving specific nonlinearities of quartic type by proposing a reduced computational matrix approach based on the generalized Mott polynomial. This method presents a reduced matrix expansion of the generalized Mott polynomial with the parameter-α, matrix equations, and Chebyshev--Lobatto collocation points. The simplicity of the method provides fast computation while eliminating an algebraic system of nonlinear equations, which arises from the matrix equation. The method also scrutinizes the consistency of the solutions due to the parameter-α. The oscillatory behavior of the obtained solutions on long time intervals is simulated via a coupled methodology involving the proposed method and Laplace-Padé technique. The convergence estimation is established via residual function. Numerical and graphical results are indicated to discuss the validity and efficiency of the method.

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Cite This Article

KÜRKÇÜ, Ö. K. (2020). A reduced computational matrix approach with convergence estimation for solving model differential equations involving specific nonlinearities of quartic type. Turkish Journal of Mathematics, Cilt: 44 - Sayı: 1, 223–239. https://ajindex.com/articles/193221

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References (13)

  1. Barker GA Jr. Essentials of Padé Approximants. San Diego, CA, USA: Academic Press, 1975. 237 [2] Baxley JV, Gu Y. Nonlinear boundary value problems for shallow membrane caps. Communications in Applied Analysis 1999
  2. Bisshopp KE, Drucker DC. Large defections of cantilever beams. Quarterly of Applied Mathematics 1954
  3. Bülbül B, Sezer M. Numerical solution of Duffing equation by using an improved Taylor matrix method. Journal of Applied Mathematics 2013: 2013
  4. 691614. doi: 10.1155/2013/691614 [5] Bülbül B, Sezer M. A numerical approach for solving generalized Abel-type nonlinear differential equations. Applied Mathematics and Computation 2015
  5. Chandrasekhar S. Introduction to the Study of Stellar Structure. New York, NY, USA: Dover, 1967. [7] Dickey RW, Rotationally symmetric solutions for shallow membrane caps. Quarterly of Applied Mathematics 1989
  6. 47 (3): 571-581. [8] Duan JS, Rach R. A new modification of the Adomian decomposition method for solving boundary value problems for higher order nonlinear differential equations. Applied Mathematics and Computation 2011
  7. Duggan R, Goodman A. Pointwise bounds for a nonlinear heat conduction model of the human head. Bulletin of Mathematical Biology 1986
  8. 48 (2): 229-236. [10] Erdèlyi A, Magnus W, Oberhettinger F, Tricomi FG. Higher Transcendental Functions. Vol. III. New York, NY, USA: McGraw-Hill Book Company, 1955. [11] Giné J, Valls C. On the dynamics of the Rayleigh–Duffing oscillator. Nonlinear Analysis Real World Applications 2019
  9. Gümgüm S, Savaşaneril NB, Kürkçü ÖK, Sezer M. A numerical technique based on Lucas polynomials together with standard and Chebyshev-Lobatto collocation points for solving functional integro-differential equations involving variable delays. Sakarya University Journal of Science 2018
  10. 22 (6): 1659-1668. [13] Haq S, Ishaq M. Solution of strongly nonlinear ordinary differential equations arising in heat transfer with optimal homotopy asymptotic method. International Journal of Heat and Mass Transfer 2012
  11. He JH. Some asymptotic methods for strongly nonlinear equations. International Journal of Modern Physics B 2006
  12. 20 (10): 1141-1199. [15] Kanth ASVR, Aruna K. He’s variational iteration method for treating nonlinear singular boundary value problems. Computers & Mathematics with Applications 2010
  13. Kruchinin DV. Explicit formula for generalized Mott polynom