Numerical Solution of Eighth Order Two Point Boundary Value Problems by Taylor Series Method
DOI:
https://doi.org/10.56919/usci.2431.006Keywords:
Taylor series, eighth order boundary value problems, successive differentiating, two point boundary value problemAbstract
A Taylor series method which is taught at undergraduate levels and which has been hitherto used for the solution of initial value problem is successfully used in this work for the solutions of eighth-order two point boundary-value problems. The method is based on successive differentiation of the governing equation to obtain high order derivatives and then evaluated at the boundary point x=a. The solution is expressed inform a Taylor series with the unknown coefficients at a point x=a. By applying boundary conditions at x=b in the Taylor series solution, the system of unknown coefficient is obtained. After solving the system, then unknown coefficient are determined. The procedure is applied on both linear and nonlinear boundary-value problems. A comparison of the results obtained by the present method with results obtained by other methods reveals that the present method is simple, effective and also is in good agreement with the previous result and exact solution as showing in the tables and figures.
References
Agarwal, R.P. (1986). Boundary value problems for Higher Order Differential Equations, World https://doi.org/10.1142/0266
Amin, R., Shah, K. Al-mdallal Q.M.,Khan, I. and Asif M. (2021). Efficient Numerical algorithm for the solution of eight order boundary value problems by Harr wavelet method, Int. J. App. Comput. Math.7:34 https://doi.org/10.1007/s40819-021-00975-x
Chandrasekhar, S. (1961): Hydrodynamic and Hydromagnetic Stability. Clarendon Press, Oxford .
Elahi,Z.Akram,G. and Siddiqi,S.S.,(2016): Numerical solution for solving special eighth-order linear boundary value problems using legendre Galerkin method. Math. Sci https://doi.org/10.1007/540096_016_0194_9.
El-Gamel M and Abdrabou A Sinc-Galerkin solution to eighth-order boundary value problems SeMA Journal 76:249–270 (2019) . https://doi.org/10.1007/s40324-018-01722
Haq S. and Sohaib M. (2021). An enhanced wavelet based method for numerical solution of high order boundary value problems J. mt. area res., Vol. 6, https://doi.org/10.53874/jmar.v6i0.109
He J. H (2007.). The variation iteration method for eighth _order initial_boundary value problems phys. Scr. 76(680_682) https://doi.org/10.1088/0031-8949/76/6/016
He J. H., (2020): Taylor series solution for a third order boundary valued problems arising in Architecture Engineering. AIN shams Engineering journals 11 1411-1414. https://doi.org/10.1016/j.asej.2020.01.016
Khalid, A., Naeem, M.N., Uilah, Z. Ghaffar, A. Balean, D.,Nasar K.S., and Alqurashi M.M, .(2019). Numerical solution of the boundary value problems arising in magnetic field and cylindrical shells . J. Math. 34k10. https://doi.org/10.3390/math7060508
Mestrovi c M. (2007). The modified decomposition method for eighth _order boundary value problems. Apply. Math. Comput.(1437_1444) 34,k12. https://doi.org/10.1016/j.amc.2006.11.015
Mamun A. AL, Asaduzzaman M., Ananna Nahar samsun. (2019). Solution of Eighth Order Boundary Value Problem by Using Variational Iteration Method International journal of mathematic and computational science vol. 5 No 1 pp. 13-23, http://www.aiscience.org/journal/ijmcs
Porshokouhi, M.G, Ghanbar B., Ghotaml M. and Rashidi M. (2011). Numerical solution of Eighth order boundary value problems with variational iteration method. Gen. Math. Note vol. 2 No. 1 pp128_133 http://www.geman.in
Reddy A P, Haranjula MS. and Sateesha C. ( 2017). Numerical approach to solve 8th order boundary value problems by Harr wavelet collocation method. J. Math. Model Vol.5 https://doi.org/10.13140/RG.2.2.24075.95527.
Raji T. M. Ishola Y. C., Babalola O.O, Ayoola A. T., Momoh M N, and Peter J.O. (2023). Numerical solution of eight order boundary value problems using Chebyshev polynomials Mathematics and Computational Sciences, Vol 4(1) https://doi.org/10.30511/mcs.2023.1988829.1108
Siddiqi, S.S and Iftikhar,M. (2013). Numerical solution or higher order boundary value problems. Abstract and Applied Analysis hindawi publishing corporations volumes 2013, Arlicce ID427521, 12 pages, https://doi.org/10.1155/2013/427521
Twizell L,E.H,. Bountayeb, A. and Djdjelik, K.( 1994) Numerical methods for eighth, tenth, and twelfill order eigen value problems arising in thermal instability, Advances in compulationary mathematics 2(407_436).
Xu, X. And Zhou F.(2015). Numerical solution for the eighth_order initial and boundary value problems using the second kind chebyshell waicelet Advances in mathematical physics volume Articles ID 964623, 9pages https://doi.org/10.1155/2015/964623
Downloads
Published
How to Cite
Issue
Section
License
Copyright (c) 2024 UMYU Scientifica
This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.
