References
References
- Bellman RE Kalaba RE (1965) Quasilinearization and Nonlinear Boundary-Value Problems, American Elsevier New York
- Cunningham WJ (1958) Introduction to Nonlinear Analysis, McGraw-Hill Book Company, Inc New York
- Doolan EP Miller JJH Schilders WHA (1980) Uniform Numerical Methods for Problems with Initial and Boundary Layers, Boole Press Dublin
- Farrell , PA . (1987) . Sufficient conditions for uniform convergence of a class of difference schemes for a singularly perturbed problem . IMA, J. Numer. Anal. , 7 : 459 – 472 .
- Farrell PA Hegarty AF Miller JJH O'Riordan E Shishkin GI (2000) Robust Computational Techniques for Boundary Layers, CRC Press LLC Boca Raton FL
- Farrell , PA , Miller , JJH , O'Riordan , E and Shishkin , GI . (1996) . A uniformly convergent finite difference scheme for a singularly perturbed semilinear equation . SIAM, J. Numer. Anal. , 33 : 1135 – 1149 .
- Farrell , PA , Miller , JJH , O'Riordan , E and Shishkin , GI . (1998) . On the non-existence of ϵ-uniform finite difference methods on uniform meshes for semilinear equation . SIAM, J. Numer. Anal. , 67 : 603 – 617 .
- Kellogg , RB and Tsan , A . (1978) . Analysis of some difference approximations for a singular perturbation problem without turning points . Math. Comp. , 32 : 1025 – 1039 .
- Lange , CG and Miura , RM . (1991) . Singular perturbation analysis of boundary-value problems for differential-difference equations. iv. a nonlinear example with layer behavior . Studies Appl. Math. , 84 : 231 – 273 .
- Miller JJH Mullarkey E O'Riordan E Shishkin GI (1991) A simple recipe for uniformly convergent finite difference schemes for singularly perturbed problems, C. R. Acad. Sci. Paris, t 312, Série I pp. 643–648
- Miller JJH O'Riordan E Shishkin G (1996) Fitted Numerical Methods for Singularly Perturbed Problems: Error Estimates in the Maximum Norm for Linear Problems in One and Two Dimension, World Scientific Publication Singapore
- O'Riordan , E and Stynes , M . (1986) . A uniformly accurate finite-element method for a singularly perturbed one-dimensional reaction-diffusion problem . Math. Comput. , 47 : 555 – 570 .
- Roos HG Stynes M Tobiska L (1996) Numerical Methods for Singularly Perturbed Differential Equations: Convection–Diffusion and Flow Problems, Springer-Verlag New York
- Shishkin , GI . (1988) . A difference scheme for a singularly pertubed equation of parabolic type with a discontinuous initial condition . Soviet Math. Dokl. , 37 : 792 – 796 .