An asymptotic initial value method for second order singular perturbation problems of convection-diffusion type with a discontinuous source term (original) (raw)

Access this article

Log in via an institution

Subscribe and save

• Starting from 10 chapters or articles per month
• Access and download chapters and articles from more than 300k books and 2,500 journals
• Cancel anytime View plans

Buy Now

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

References

1. A. H. Nayfeh,Introduction to Perturbation Methods, John Wiley and Sons, New York, 1981.
   Google Scholar
2. J. J. H. Miller, E. O’Riordan and G. I. Shishkin,Fitted Numerical Methods for Singular Perturbation Problems: Error Estimates in the Maximum Norm for Linear Problems in One and Two Dimensions, World Scientific Publishing Co. Pte. Ltd, 1996.
3. H.-G. Roos, M. Stynes and L. Tobiska,Numerical Methods for Singularly Perturbed Differential Equations, Springer, New York, 1996.
   MATH Google Scholar
4. E. P. Doolan, J. J. H. Miller and W. H. A. Schilders,Uniform Numerical Methods for Problems with Initial and Boundary Layers, Boole Press, Dublin, 1980.
   MATH Google Scholar
5. P. A. Farrell, A. F. Hegarty, J. J. H. Miller, E. O’Riordan and G. I. Shishkin,Robust Computational Techniques for Boundary Layers, Chapman and Hall/CRC, Boca Ration, FL, 2000.
   MATH Google Scholar
6. P. A. Farrel, J. J. H. Miller, E. O’ Riordan and G. I. Shishkin,Singularly Perturbed Differential Equations with Discontinuous Source Terms, Proceedings of “Analytical and Numerical Methods for Convection-Dominated and Singularly Perturbed Problems”, Lozenetz, Bulgaria, 1998, J. J. H. Miller, G.I. Shishkin and L. Vulkov eds., Nova Science Publishers. New York, 23–32, USA (2000).
   Google Scholar
7. P. A. Farrel, A. F. Hegarty, J. J. H. Miller, E. O’ Riordan and G. I. Shishkin,Global Maximum Norm Parameter- Uniform Numerical Method for a Singularly Perturbed Convection-Diffusion Problem with Discontinuous Convection Coefficient, Mathematical and Computer Modelling40 (2004), 1375–1392.
   Article MathSciNet Google Scholar
8. P. A. Farrel, A. F. Hegarty, J. J. H. Miller, E. O’ Riordan and G. I. Shishkin,Singularly Perturbed Convection Diffusion Problems with Boundary and Weak Interior Layers, Journal of Computational Applied Mathematics166(1) (2004), 133–151.
   Article Google Scholar
9. J. H. Miller, E. O’Riordan and S. Wang,A Parameter-Uniform Schwartz Method for a Singularly Perturbed Reaction-Diffusion Problem with an Interior Layer, Applied Numerical Mathematics35 (2000), 323–337.
   Article MATH MathSciNet Google Scholar
10. A.-G. Roos and H. Zarin,A second order scheme for Singularly Perturbed Differential Equations with Discontinuous Source Term, J. Numer. Math.10 (2002), 275–289.
    MATH MathSciNet Google Scholar
11. M. G. Gasparo and M. Macconi,Initial-Value Methods for Second Order Singularly Perturbed Boundary-Value Problems, J1. of Optimization Theory and Applications66 (1990), 197–210.
    Article MATH MathSciNet Google Scholar
12. M. G. Gasparo and M. Macconi,Parallel Initial-Value Algorithms for Singularly Perturbed Boundary-Value Problems, J. of Optimization Theory and Applications73 (1992), 501–517.
    Article MATH MathSciNet Google Scholar
13. S. Natesan and N. Ramanujam,Initial-Value Technique for Singularly-perturbed Turning Point Problem Exhibiting Twin Boundary Layers, J. of Optimization Theory and Applications99 (1998), 37–52.
    Article MATH MathSciNet Google Scholar
14. S. Natesan and N. Ramanujam,Initial-Value Technique for Singularly-Perturbed Boundary-Value Problems for Second Order Ordinary Differential Equations Arising in Chemical Reactor Theory, J. of Optimization Theory and Applications97 (1998), 455–470.
    Article MATH MathSciNet Google Scholar
15. T. Valanarasu and N. Ramanujam,Asymptotic Initial Value Methods for Two-Parameter Singularly Perturbed Boundary Value Problems for Second Order Ordinary Differential Equations, Applied Mathematics and Computation137 (2003), 549–570.
    Article MATH MathSciNet Google Scholar
16. T. Valanarasu and N. Ramanujam,Asymptotic Initial-Value Method for Singularly- Perturbed Boundary-Value Problems for Second-Order Ordinary Differential Equations, J. of Optimization Theory and Applications116 (2003), 167–182.
    Article MATH MathSciNet Google Scholar
17. T. Valanarasu and N. Ramanujam,An Asymptotic Initial Value Method for Boundary Value Problems for a System of Singularly Perturbed Second Order Ordinary Differential Equations, Applied Mathematics and Computation147 (2004). 227–240.
    Article MATH MathSciNet Google Scholar
18. T. Valanarasu and N. Ramanujam,Asymptotic Initial Value Method for a System of Singularly Perturbed Second Order Ordinary Differential Equations of Convection Diffusion Type, Int. J. of Computer Mathematics81 (2004), 1381–1393.
    Article MATH MathSciNet Google Scholar

Download references