By Valarmathi Sigamani, John J. H. Miller, Ramanujam Narasimhan, Paramasivam Mathiazhagan, Franklin Victor
This ebook deals a terrific creation to singular perturbation difficulties, and a worthy advisor for researchers within the box of differential equations. it's also chapters on new contributions to either fields: differential equations and singular perturbation difficulties. Written via specialists who're lively researchers within the comparable fields, the e-book serves as a complete resource of data at the underlying principles within the building of numerical the way to tackle various periods of issues of ideas of alternative behaviors, so that it will eventually support researchers to layout and investigate numerical tools for fixing new difficulties. all of the chapters offered within the quantity are complemented by way of illustrations within the type of tables and graphs.
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Extra info for Differential Equations and Numerical Analysis: Tiruchirappalli, India, January 2015
Math. Comput. 219(2), 498–510 (2012) 25. A. Farrell, E. I. Shishkin, A class of singularly perturbed semilinear differential equations with interior layers. Math. Comp. 74, 1759–1776 (2005) 26. N. Kopteva, M. Stynes, Stabilised approximation of interior-layer solutions of a singularly perturbed semilinear reaction-diffusion problem. Numer. Math. 119, 787–810 (2011) 27. A. Farrell, E. I. Shishkin, A class of singularly perturbed quasilinear differential equations with interior layers. Math. Comp.
By placing further restrictions on the data, a parameter-uniform method was constructed in  for this semilinear problem. However, other semilinear problems of the form (11) can be very difficult to solve numerically. In  a semilinear problem of the form (11) with smooth data, where an unstable continuous reduced solution was positioned between two stable continuous reduced solutions, was examined. Using a piecewise-uniform Shishkin mesh (of an appropriate width) centered at any point in the domain Ω, then an interior layer forms within the fine mesh, no matter where the mesh is √ centered .
L. Gracia, E. O’Riordan, A singularly perturbed convection–diffusion problem with a moving interior layer. Int. J. Numer. Anal. Model. 9(4), 823–843 (2012) 24. L. Gracia, E. O’Riordan, A singularly perturbed parabolic problem with a layer in the initial condition. Appl. Math. Comput. 219(2), 498–510 (2012) 25. A. Farrell, E. I. Shishkin, A class of singularly perturbed semilinear differential equations with interior layers. Math. Comp. 74, 1759–1776 (2005) 26. N. Kopteva, M. Stynes, Stabilised approximation of interior-layer solutions of a singularly perturbed semilinear reaction-diffusion problem.