A computational method for solving third-order singularly perturbed boundary-value problems

Applied Mathematics and Computation

Volumn 198, Issue 2, 2008, Pages 896-903

  Cui, M ^a   Geng, F ^a  

^a HARBIN INSTITUTE OF TECHNOLOGY   (China)

Author keywords

Analytical solution; Asymptotic expansion; Reproducing kernel; Third order singularly perturbed boundary value problems

Indexed keywords

ASYMPTOTIC ANALYSIS; BOUNDARY CONDITIONS; BOUNDARY LAYERS; BOUNDARY VALUE PROBLEMS; PROBLEM SOLVING;

ASYMPTOTIC EXPANSION; KERNEL SPACES; REPRODUCING KERNELS; TERMINAL VALUE PROBLEMS; THIRD ORDER SINGULARLY PERTURBED BOUNDARY VALUE PROBLEMS;

COMPUTATIONAL METHODS;

EID: 40849132839     PISSN: 00963003     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.amc.2007.09.023     Document Type: Article

References (20)

1. Roos H.G., Stynes M., and Tobiska L. Numerical Methods for Singularly Perturbed Differential Equations (1996), Springer-Verlag
2. Howes F.A. Singular Perturbations and Differential Inequalities (1976), Memoirs of the American Mathematical Society, Providence, Rhode Island p. 168
3. Ascher V., and Weiss R. Collocation for singular-perturbation problems, III: nonlinear problems without turning points. SIAM Journal on Scientific and Statistical Computing 5 (1984) 811-829
4. Kadalbajoo M., and Aggarwal V.K. Fitted mesh B-spline collocation method for solving self-adjoint singularly perturbed boundary value problems. Applied Mathematics and Computation 161 (2005) 973-987
5. Roos H.G. A second-order monotone upwind scheme. Computing 36 (1986) 57-67
6. Ilicasu F.O., and Schultz D.H. High-order finite-difference techniques for linear singular perturbation boundary value problems. Computers and Mathematics with Applications 47 (2004) 391-417
7. Stynes M., and O'Riordan E. A uniformly accurate finite-element method for a singular-perturbation problem in conservative form. SIAM Journal on Numerical Analysis 23 (1986) 369-375
8. Vigo-Aguiar J., and Natesan S. A parallel boundary value techniques for singularly perturbed two-point boundary value problems. The Journal of Supercomputing 27 (2004) 195-206
9. Reddy Y.N., and Chakravarthy P.P. An initial-value approach for singularly perturbed two-point boundary value problems. Applied Mathematics and Computation 155 (2004) 95-110
10. Valanarasu T., and Ramanujam N. Asymptotic initial-value method for singularly-perturbed boundary-value problems for second-order ordinary differential equations. Journal of Optimization Theory and Applications 116 (2003) 167-182
11. Bawa R.K. Spline based computational technique for linear singularly perturbed boundary value problems. Applied Mathematics and Computation 167 (2005) 225-236
12. Aziz T., and khan A. A spline method for second-order singularly perturbed boundary-value problems. Journal of Computational and Applied Mathematics 147 (2002) 445-452
13. Howes F.A. Differential inequalities of higher order and the asymptotic solution of nonlinear boundary value problems. SIAM Journal on Mathematical Analysis 131 (1982) 61-80
14. Howes F.A. The asympototic solution of a class of third-order boundary problem arising in the theory of thin film flow. SIAM Journal of Applied Mathematics 43 5 (1983) 993-1004
15. Weili Z. Singular perturbations of boundary value problems for a class of third order nonlinear ordinary differential equations. Journal of Differential Equations 88 2 (1990) 265-278
16. Roberts S.M. Further examples of the boundary value technique in singular perturbation problems. Journal of Mathematical Analysis and Applications 133 (1988) 411-436
17. Valarmathi S., and Ramanujam N. A computational method for solving boundary value problems for third-order singularly perturbed ordinary differential equations. Applied Mathematics and Computation 129 (2002) 345-373
18. Nayfeh A.H. Introduction to Perturbation Method (1981), Wiley, New York
19. Natesan S., and Ramanujam N. A computational method for solving singularly perturbed turing point problems exhibiting twin boundary layer. Applied Mathematics and Computation 93 (1998) 259-275
20. Li C., and Cui M. The exact solution for solving a class nonlinear operator equations in the reproducing kernel space. Applied Mathematics and Computation 143 2-3 (2003) 393-399