Reproducing kernel method for singularly perturbed turning point problems having twin boundary layers

Applied Mathematics Letters

Volumn 26, Issue 10, 2013, Pages 998-1004

  Geng, F Z ^a   Qian, S P ^a  

^a CHANGSHU INSTITUTE OF TECHNOLOGY   (China)

Author keywords

Reproducing kernel method; Singularly perturbed problems; Turning point; Twin boundary layers

Indexed keywords

NUMERICAL METHODS; PERTURBATION TECHNIQUES;

APPROXIMATE SOLUTION; DOMAIN PROBLEMS; FIRST DERIVATIVE; REPRODUCING KERNEL METHODS; SINGULARLY PERTURBED; SINGULARLY PERTURBED PROBLEM; TRANSITION POINT; TURNING POINTS;

BOUNDARY LAYERS;

EID: 84886945821     PISSN: 08939659     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.aml.2013.05.006     Document Type: Article

References (24)

1. K. Phaneendra, Y.N. Reddy, GBSL Soujanya, Non-iterative numerical integration method for singular perturbation problems exhibiting internal and twin boundary layers, Int. J. Appl. Math. Comput. 3 (2011) 9-20.
2. P. Rai, K.K. Sharma, Numerical method for singularly perturbed differential-difference equation with turning point, Int. J. Pure Appl. Math. 73 (2011) 451-470.
3. P. Rai, K.K. Sharma, Numerical study of singularly perturbed differential-difference equation arising in the modeling of neuronal variability, Comput. Math. Appl. 63 (2012) 118-132.
4. P. Rai, K.K. Sharma, Numerical analysis of singularly perturbed delay differential turning point problem, Appl. Math. Comput. 218 (2011) 3483-3498.
5. S. Natesan, J. Jayakumar, J. Vigo-Aguiar, Parameter uniform numerical method for singularly perturbed turning point problems exhibiting boundary layers, J. Comput. Appl. Math. 158 (2003) 121-134.
6. M.K. Kadalbajoo, P. Arora, V. Gupta, Collocation method using artificial viscosity for solving stiff singularly perturbed turning point problem having twin boundary layers, Comput. Math. Appl. 61 (2011) 1595-1607.
7. M.G. Cui, Y.Z. Lin, Nonlinear Numerical Analysis in Reproducing Kernel Space, Nova Science Pub. Inc., 2009.
8. A. Berlinet, Christine Thomas-Agnan, Reproducing Kernel Hilbert Space in Probability and Statistics, Kluwer Academic Publishers, 2004.
9. B.Y. Wu, X.Y. Li, Iterative reproducing kernel method for nonlinear oscillator with discontinuity, Appl. Math. Lett. 23 (2010) 1301-1304.
10. X.Y. Li, B.Y. Wu, Error estimation for the reproducing kernel method to solve linear boundary value problems, J. Comput. Appl. Math. 243 (2013) 10-15.
11. H.M. Yao, Solution of the Duffing equation involving both integral and non-integral forcing terms, Comput. Phys. Comm. 180 (2009) 1481-1488.
12. F.Z. Geng, M.G. Cui, Solving a nonlinear system of second order boundary value problems, J. Math. Anal. Appl. 327 (2007) 1167-1181.
13. M.G. Cui, F.Z. Geng, Solving singular two-point boundary value problem in reproducing kernel space, J. Comput. Appl. Math. 205 (2007) 6-15.
14. F.Z. Geng, M.G. Cui, New method based on the HPM and RKHSM for solving forced Duffing equations with integral boundary conditions, J. Comput. Appl. Math. 233 (2009) 165-172.
15. F.Z. Geng, M.G. Cui, A novel method for nonlinear two-point boundary value problems: combination ofADMand RKM, Appl. Math. Comput. 217 (2011) 4676-4681.
16. F.Z. Geng, A numerical algorithm for nonlinear multi-point boundary value problems, J. Comput. Appl. Math. 236 (2012) 1789-1794.
17. M. Mohammadi, R. Mokhtari, Solving the generalized regularized long wave equation on the basis of a reproducing kernel space, J. Comput. Appl. Math. 235 (2011) 4003-4014.
18. Y. Zhou, M.G. Cui, Y. Lin, Numerical algorithm for parabolic problems with non-classical conditions, J. Comput. Appl. Math. 230 (2009) 770-780.
19. G. Akram, H. Ur Rehman, Numerical solution of eighth order boundary value problems in reproducing kernel space, Numer. Algorithms (2012) http://dx.doi.org/10.1007/s11075-012-9608-4.
20. O.A. Arqub, M. Al-Smadi, S. Momani, Application of reproducing kernel method for solving nonlinear Fredholm-Volterra integro-differential equations, Abstr. Appl. Anal. 2012 (2012) 1-16.
21. K. Özen, K. Oruço?lu, Investigation of numerical solution for fourth-order nonlocal problem by the reproducing kernel method, AIP Conf. Proc. 1389 (2011) 1164-1167.
22. W.Y. Wang, B. Han, M. Yamamoto, Inverse heat problem of determining time-dependent source parameter in reproducing kernel space, Nonlinear Anal. RWA 14 (2013) 875-887.
23. F.Z. Geng, M.G. Cui, A novel method for solving a class of singularly perturbed boundary value problems based on reproducing kernel method, Appl. Math. Comput. 218 (2011) 4211-4215.
24. R. Mokhtari, F.T. Isfahani, M. Mohammadi, Reproducing kernel method for solving nonlinear differential-difference equations, Abstr. Appl. Anal. 2012 (2012) 1-10.