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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, Ireland, 1980.
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A.H. Nayfeh, Introduction to perturbation methods, John Wiley and Sons, New York, 1981.
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R.E. O'Malley, Singularly perturbation method for ordinary differential equation, Springer Verlag, New York, 1991.
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H.G. Roos, M. Stynes and L. Tobiska, Numerical methods for singularly perturbed differential equations Springer, New York, 1996.
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J.J. H. Miller, E. O'Riordan and G.I. Shishkin, Fitted numerical methods for singular perturbation problem, World Scientific, Singapore, 1996.
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M.K. Kadalbajoo and V. Gupta, A brief survey of numerical methods for solving singularly perturbed problems, Applied Mathematics and Computation 217 (2010), 3641–3716.
DOI
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M. Paramasivam, S. Valarmathi and J.J.H. Miller, Second-order parameter uniform convergence for finite difference method for singularly perturbed linear differential equation, Mathematical Communications 15 (2010), 587–612.
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J.J.H. Miller, E. O’Riordan, G.I. Shishkin and S. Wang, A parameter-uniform Schwarz method for a singularly perturbed reaction-diffusion problem with an interior layer, Applied Numerical Mathematics 35 (2000), 323–337.
DOI
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N. Kopteva, M. Pickett and H. Purtill, A robust overlapping Schwarz method for a singularly perturbed semilinear reaction-diffusion problem with multiple solutions, Int. J. Numer. Anal. Model. 6 (2009), 680–695.
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10 |
M. Chandru and V. Shanthi, A boundary value technique for singularly perturbed boundary value problem of reaction-diffusion with non-smooth data, Journal of Engineering Science and Technology, Special Issue on ICMTEA2013 Conference (2014), 32-45.
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M. Chandru, T. Prabha and V. Shanthi, A Hybrid Difference Scheme For A second-order singularly perturbed reaction-diffusion problem with non-smooth data, Int. J. Appl. Comput. Math. 1 (2015), 87–100.
DOI
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M. Chandru and V. Shanthi, Fitted mesh method for singularly perturbed Robin type boundary value problem with discontinuous source term, Int. J. Appl. Comput. Math. 1 (2015), 491–501.
DOI
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M. Chandru, T. Prabha and V. Shanthi, A parameter robust higher order numerical method for singularly perturbed two parameter problems with non-smooth data, Journal of Computational and Applied Mathematics(Accepted), DOI:10.1016/j.cam.2016.06.009.
DOI
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S. Valarmathi and N. Ramanujam, An asymptotic numerical fitted mesh method for singularly perturbed third-order ordinary differential equations of reaction-diffusion type, Applied Mathematics and Computation 132 (2002), 87–104.
DOI
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V. Shanthi and N. Ramanujam, An asymptotic numerical method for fourth-order singular perturbation problems with a discontinuous source term, International Journal of Computer Mathematics 55 (2008), 1147–1159.
DOI
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V. Shanthi and N. Ramanujam, A numerical method for boundary value problems for singularly perturbed fourth-order ordinary differential equations, Applied Mathematics and Computation 129 (2002), 269–294.
DOI
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V. Shanthi and N. Ramanujam, Asymptotic numerical method for singularly perturbed fourth-order ordinary differential equations of reaction-diffusion type, Computers & Mathematics with Applications 46 (2003), 463–478.
DOI
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V. Shanthi and N. Ramanujam, Computational methods for reaction-diffusion problems for fourth-order ordinary differential equations with a small parameter at the highest derivative, Applied Mathematics and Computation 147 (2004), 97–113.
DOI
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P.A. Farrell, J.J.H. Miller, E. O'Riordan and G.I. Shishkin, Singularly perturbed differential equations with discontinuous source terms, In Proc. Lozenetz 2 (2000).
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