Taylor Collocation Method for Nonlinear System of SecondOrder Boundary Value Problems
Abstract
In this study, a numerical approach is proposed to obtain approximate solutions of nonlinear system of secondorder boundary value problem. This technique is essentially based on the truncated Taylor series and its matrix representations with collocation points. Using the matrix method, we reduce the problem system of nonlinear algebraic equations. Numerical examples are also given to demonstrate the validity and applicability of the presented technique. The method is easy to implement and produces accurate results. All numerical computations have been performed on the computer algebraic system Maple 9.
Keywords
Nonlinear system, Second-order boundary value problem, Taylor polynomials and series, Collocation points
References
- S. Matthews, Parameter robust numerical methods for a system of two coupled singularly perturbed reaction–diffusion equations, M.Sc. Thesis, School of Mathematical Sciences, Dublin City University, (2000).
- C. Wafo Soh, F.M. Mahomed Internat. J. Non-Linear Mech. 36 (2001) 671.
- K.W. Tomantschger J. Comput. Appl. Math. 140 (2002) 773.
- D.D. Ganji, A. Sadighi Int. J. Nonlinear Sci. Numer. Simul. 7 (2006) 411.
- A.M. Wazwaz Appl. Math. Comput. 128 (2002) 45.
- J.I. Ramos Appl. Math. Comput. 161 (2005) 525.
- F. Geng, M. Cui J. Math. Anal. Appl. 327 (2007) 1167.
- J. Lu Comput. and Math. with Appl. 54 (2007) 1133.
- M. Dehghan, A. Saadatmandi Math. Comput. Modelling 46 (2007) 1434.
- A. Saadatmandi, J. A. Farsangi Appl. Math. Comput. 192(2) (2007) 586.