International Journal of Mathematical Sciences and Computing (IJMSC)
IJMSC Vol. 7, No. 1, 8 Feb. 2021
Cover page and Table of Contents: PDF (size: 815KB)
Concepts of Bezier Polynomials and its Application in Odd Higher Order Non-linear Boundary Value Problems by Galerkin WRM
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Author(s)
Nazrul Islam
1,*
Index Terms
Higher order non-linear differential equations, Numerical solutions, Galerkin method, Bezier polynomials.
Abstract
Many different methods are applied and used in an attempt to solve higher order nonlinear boundary value problems (BVPs). Galerkin weighted residual method (GWRM) are widely used to solve BVPs. The main aim of this paper is to find the approximate solutions of fifth, seventh and ninth order nonlinear boundary value problems using GWRM. A trial function namely, Bezier Polynomials is assumed which is made to satisfy the given essential boundary conditions. Investigate the effectiveness of the current method; some numerical examples were considered. The results are depicted both graphically and numerically. The numerical solutions are in good agreement with the exact result and get a higher accuracy in the solutions. The present method is quit efficient and yields better results when compared with the existing methods. All problems are performed using the software MATLAB R2017a.
Cite This Paper
Nazrul Islam," Concepts of Bezier Polynomials and its Application in Odd Higher Order Non-linear Boundary Value Problems by Galerkin WRM ", International Journal of Mathematical Sciences and Computing(IJMSC), Vol.7, No.1, pp. 11-19, 2021. DOI: 10.5815/ijmsc.2021.01.02
Reference
[1]Wazwaz A.M., The numerical solution of fifth order boundary value problems by the decomposition method, Journal of Computational and Applied Mathematics, 136, 2001, 259-270.
[2]Erturk V.S., Solving nonlinear fifth order boundary value problems by differential transformation method, Selcuk J. Appl. Math., 8(1), 2007, 45-49.
[3]Siddiqi S. S., Ghazala Akram and Muzammal I., Solution of seventh order boundary value problems by variational iteration technique, Applied Mathematical Sciences, 6(94), 2012, 4663-4672.
[4]Ghazala Akram, Siddiqi S. S., Nonic spline solutions of eighth-order boundary value problems, Appl. Math. and Computational, 182, 2006, 829-845.
[5]Agarwal R.P., Boundary Value Problems for Higher Order Differential Equations, World Scientific, Singapore, 1986.
[6]Siddiqi S. S. and Muzammal I., Solution of seventh order boundary value problem by variation of parameters method, Research Journal of Applied Sciences, Engineering and Technology, 5(1), 2013, 176-179.
[7]Djidjeli K., Twizell E.H. and Boutayeb A., Numerical methods for special nonlinear boundary value problems of order 2m, J. Comput. Appl. Math., 47, 1993, 35-45.
[8]Noor M.A. and Mohyud-Din S.T., Homotopy perturbation method for nonlinear higher order boundary value problems, Int. J. Nonlinear Sci. Num. Simul., 9, 2008, 395-408.
[9]Mohyud-Din S.T., Noor M.A. and Noor K.I., Traveling wave solutions of seventh order generalized KdV equations using He’s polynomials, Int. J. Nonlinear Sci. Num. Sim., 10, 2009, 223-229.
[10]Mohyud-Din S.T., Solution of nonlinear differential equations by ex-function method, World Applied Sciences Journal, 7, 2009, 116-147.
[11]Wazwaz A.M., The modified decomposition method for solving linear and nonlinear boundary value problems of tenth order and twelfth order, Int. J. Nonlinear Sci. Num. Sim., 1, 2008, 17-24.
[12]Reddy P.A., Sateesha A., Manjula S.H., Investigation of haar wavelet Collocation method to solve ninth order boundary value problems, Global Journal of Pure and Applied Mathematics, 13, 2017, 1415-1428.
[13]Hossain, M.B., Islam, M.S., A novel numerical approach for odd higher order boundary value problems, Mathematical Theory and Modeling, 4(5), 2014, 2224-5804.
[14]Kasi Viswanadham, K. N. S., Reddy, S. M., Numerical solution of ninth order boundary value problems by Petrov-Galerkin method with Quintic B-splines as basis functions and Septic B-splines as weight functions, Elsevier, 127 , 2015, 1227 – 1234.
[15]Mohyud-Din S.T. and Yildirim A., Solutions of tenth and ninth order boundary value problems by modified variational iteration method, Applications and Applied Mathematics, 5 (1), 2010, 11-25.
[16]Mohamed Othman I.A., Mahdy A.M.S. and Farouk R.M., Numerical solution of 12th order boundary value problems by using homotopy perturbation method, The Journal of Mathematics and Computer Science, 1 (1), 2010, 14- 27.
[17]Nadjafi J.S. and Zahmatkesh S., Homotopy perturbation method (HPM) for solving higher order boundary value problems, Applied Mathematical and Computational Sciences, 1 (2), 2010, 199-224.