Parameter-uniform numerical methods for some linear and nonlinear singularly perturbed convection diffusion boundary turning point problems
- 112 Downloads
Both linear and nonlinear singularly perturbed two point boundary value problems are examined in this paper. In both cases, the problems have a boundary turning point and are of convection-diffusion type. Parameter-uniform numerical methods composed of monotone finite difference operators and piecewise-uniform Shishkin meshes, are constructed and analyzed for both the linear and the nonlinear class of problems. Numerical results are presented to illustrate the theoretical parameter-uniform error bounds established.
KeywordsSingular perturbation Shishkin mesh Nonlinear Boundary turning point
Mathematics Subject Classification (2000)65L11 65L20 65L12
Unable to display preview. Download preview PDF.
- 1.Bernfield, S.R., Lakshmikantham, V.: An Introduction to Nonlinear Boundary Value Problems. Academic Press, New York (1974) Google Scholar
- 10.Vulanović, R.: Boundary Shock problems and singularly perturbed Riccati equations. In: Hegarty, A.F., Kopteva, N., O’Riordan, E., Stynes, M. (eds.) BAIL 2008—Boundary and Interior Layers. Lecture Notes in Computational Science and Engineering, vol. 69, pp. 277–285. Springer, Berlin (2008) CrossRefGoogle Scholar