Series solutions to higher-order parametric boundary value problems

• Autorzy: Jeffrey David J. , Liang Songxin

Identyfikatory

DOI

10.17512/jamcm.2024.2.03

• Języki publikacji: EN

Abstrakty

EN

Solving boundary value problems with parameters is challenging. Based on the homotopy analysis method, explicit formulas for the approximate solutions to a class of higher-order parametric boundary value problems are obtained. These explicit formulas give more insight into the solution structures of the given problems. The effectiveness of this approach is demonstrated by solving two specific parametric boundary value problems.

Słowa kluczowe

EN

parametric boundary value problem; series solution; explicit formula; homotopy analysis method

PL

parametryczny problem wartości brzegowej; rozwiązanie szeregowe; wzór jawny; metoda analizy homotopii

• Wydawca: Wydawnictwo Politechniki Częstochowskiej
• Czasopismo: Journal of Applied Mathematics and Computational Mechanics
• Rocznik: 2024
• Tom: Vol. 23, nr 2
• Strony: 31--40
• Opis fizyczny: Bibliogr. 15 poz., rys., tab.

Twórcy

autor

Jeffrey David J.

• Department of Mathematics, Western University London, Canada

autor

Liang Songxin

• Department of Mathematics, Western University London, Canada

Bibliografia

• 1. Khan, S., & Khan, A. (2023). Non-polynomial cubic spline method for solution of higher order boundary value problems. Computational Methods for Differential Equations, 11(2), 225-240.
• 2. Yang, L.W. (2018). Existence and multiple solutions for higher order difference Dirichlet bound ary value problems. International Journal of Nonlinear Sciences and Numerical Simulation, 19(5), 539-544.
• 3. Ain, Q., Nadeem, M., Karim, S., Akgul, A., & Jarad, F. (2022). Optimal variational iteration ¨ method for parametric boundary value problem. AIMS Mathematics, 7(9), 16649-16656.
• 4. Momani, S., & Noor, M.A. (2007). Numerical comparison of methods for solving a special fourth-order boundary value problem. Applied Mathematics and Computation, 191, 218-224.
• 5. Noor, M.A., & Mohyud-Din, S.T. (2008). Homotopy perturbation method for solving sixth-order boundary value problems. Computers & Mathematics with Applications, 55, 2953-2972.
• 6. Liang, S.X., & Jeffrey, D.J. (2009). An efficient analytical approach for solving fourth order boundary value problems. Computer Physics Communications, 180, 2034-2040.
• 7. Turkyilmazoglu, M. (2015). Is homotopy perturbation method the traditional Taylor series expansion. Hacettepe Journal of Mathematics and Statistics, 44(3), 651-657.
• 8. Turkyilmazoglu, M. (2021). Nonlinear problems via a convergence accelerated decomposition method of Adomian. Computer Modeling in Engineering & Sciences, 127(1), 1-22.
• 9. Turkyilmazoglu, M. (2022). An efficient computational method for differential equations of frac tional type. Computer Modeling in Engineering & Sciences, 133(1), 47-65.
• 10. Liao, S.J. (2012). Homotopy Analysis Method in Nonlinear Differential Equations. Heidelberg: Springer & Higher Education Press.
• 11. Turkyilmazoglu, M. (2018). Convergence accelerating in the homotopy analysis method: a new approach. Advances in Applied Mathematics and Mechanics, 10(4), 925-947.
• 12. Brociek, R., Wajda, A., Błasik, M., & Słota, D. (2023). An application of the homotopy analysis method for the time- or space-fractional heat equation. Fractal and Fractional, 7(3), 224.
• 13. Yuan, Q., Kang, H.J., Zhao, Y.B., Cong, Y.Y., & Su, X.Y. (2023). Parametric resonance of multi frequency excited MEMS based on homotopy analysis method. Communications in Nonlinear Science and Numerical Simulation, 125, 107351.
• 14. Liang, S.X., & Jeffrey, D.J. (2010). Approximate solutions to a parameterized sixth order bound ary value problem. Computers & Mathematics with Applications, 59, 247-253.
• 15. Beckermann, B., & Labahn, G. (2000). Fraction-free computation of matrix rational interpolants and matrix GCDs. SIAM Journal on Matrix Analysis and Applications, 22, 114-144