Eleventh Degree Polynomial Series Solution Approach of Special Non-linear Fourth Order Boundary Value Problems
DOI:
https://doi.org/10.56919/usci.2431.005Keywords:
Eleventh degree polynomial, fourth order boundary value problems, successive differentiatingAbstract
In this paper a new eleventh degree polynomial series solution approach is developed for the solution of special non-linear fourth order boundary value problems. The method consist first of obtaining a linear differentials system of twelve equations from the boundary conditions, governing equation and its three successive derivatives which were evaluated at boundary points. Secondly we assume the approximate solution in the form of a polynomial of degree eleventh with twelve unknown coefficients. To determine the unknown coefficients we incorporate the assumed solution into linear differentials systems of twelve equations which results into a linear systems of twelve equations with twelve unknown and which can be solve uniquely. It is clear from the tables and figures that the method is in good agreement with the exact and with some existing results in the literatures. Also it can be seen from example 3.3 that the exact solution is reproduced which is an added advantage of the method.
References
Adeyeye O. and Omar Z. (2017) Solving Nonlinear Fourth-Order Boundary Value Problems Using a Numerical Approach: ( DOI: https://doi.org/10.1155/2017/4925914
Abd-Elhameed W. M.,Ahmed H. M, and Youssri H Youssri Y. H. (2016). A new generalized Jacobi Galerkin operational matrix of derivatives: two algorithms for solving fourth-order boundary value problems. Advances in Difference Equations 2016:22 DOI: https://doi.org/10.1186/s13662-016-0753-2
Audu K. J., Garba J. Tiamiyu A. T and Thomas B. A. (2022). Application of Backward Differentiation Formula on Fourth-Order Differential Equations .Journal of Science And Technology Vol. 14 No. 2 . 52-65.
Abd-Elhameed W. M., Youssri Y. H. (2020). Connection Formulae Between Generalized Lucas Polynomials and Some Jacobi Polynomials: Application to Certain Types of Fourth-Order BVPs. Int. J. Appl. Comput. Math 6:45. DOI: https://doi.org/10.1007/s40819-020-0799-4
Ertu¨rk V. S. and Momani S. (2007) Comparing numerical methods for solving fourth-order boundary value problems. Applied Mathematics and Computation 188 1963–1968 DOI: https://doi.org/10.1016/j.amc.2006.11.075
Hossain B. and Islam S. (2014) Numerical Solutions of General Fourth Order Two Point Boundary Value Problems by Galerkin Method with Legendre Polynomials. Dhaka Univ. J. Sci. 62(2): 103-108. DOI: https://doi.org/10.3329/dujs.v62i2.21973
Huiling Chen and Yujun Cui (2023).Existence and uniqueness of solutions to the nonlinear boundary value problem for fourth-order differential equations with all derivatives. Journal of Inequalities and Applications :23 DOI: https://doi.org/10.1186/s13660-022-02907-9
Mustafa G., Abbas M., Ejaz S.T., Ahmad Izani Md Ismail A.I and Khan F.(2017). A Numerical Approach Based on Subdivision Schemes for Solving Non-Linear Fourth Order Boundary Value Problems. J. Computational Analysis And Applications, Vol. 23, No.4.
Mingzhu Huang (2021) Existence of solutions for fourth-order nonlinear boundary Advances in Difference value problems. Equations:196 DOI: https://doi.org/10.1186/s13662-021-03354-4
Singh R., Kumar J. and Nelakanti G.(2014) Approximate series solution of fourth-order boundary value problems using decomposition method with Green’s function J Math Chem 52:1099–1118. DOI: https://doi.org/10.1007/s10910-014-0329-x
Sohel Md. N., Islam Md. S and Islam Md. S.(2022). Galerkin Residual Correction for Fourth Order BVP Journal of Applied Mathematics and Computation, 6(1), 127-138 DOI: https://doi.org/10.26855/jamc.2022.03.014
Thenmozhi S. and Marudai M. (2021). Solution of nonlinear boundary value problem by Siteration Journal of Applied Mathematics and Computing. 34B15 · 34B27 · 65L10
Viswanadham, K.N.S.K., Krishna, P.M., Koneru, R.S.: (2010) Numerical solutions of fourth order boundary value problems by Galerkin method with Quintic B-splines. Int. J. Nonlinear Sci. 10, 222–230
Wazwaz A. (2002). The Numerical solution of special fourth order boundary value problems by the modified decomposition method . Intern.J. Math. Vol. 79(3), pp. 345-356. DOI: https://doi.org/10.1080/00207160211928
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