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Numerical treatment of a quasilinear initial value problem with boundary layer
- Publication Year :
- 2016
- Publisher :
- Taylor & Francis Ltd, 2016.
-
Abstract
- The paper deals with the singularly perturbed quasilinear initial value problem exhibiting initial layer. First the nature of solution of differential problem before presenting method for its numerical solution is discussed. The numerical solution of the problem is performed with the use of a finite-fitted difference scheme on an appropriate piecewise uniform mesh (Shishkin-type mesh). An error analysis shows that the method is first-order convergent except for a logarithmic factor, in the discrete maximum norm, independently of the perturbation parameter. Finally, numerical results supporting the theory are presented. The paper deals with the singularly perturbed quasilinear initial value problem exhibiting initial layer. First the nature of solution of differential problem before presenting method for its numerical solution is discussed. The numerical solution of the problem is performed with the use of a finite-fitted difference scheme on an appropriate piecewise uniform mesh (Shishkin-type mesh). An error analysis shows that the method is first-order convergent except for a logarithmic factor, in the discrete maximum norm, independently of the perturbation parameter. Finally, numerical results supporting the theory are presented.
- Subjects :
- Singular perturbation
Logarithm
uniformly convergence
Applied Mathematics
Mathematical analysis
Perturbation (astronomy)
Shishkin mesh
initial layer
010103 numerical & computational mathematics
01 natural sciences
Computer Science Applications
010101 applied mathematics
Boundary layer
Computational Theory and Mathematics
Error analysis
Norm (mathematics)
Piecewise
Initial value problem
0101 mathematics
exponentially fitted difference scheme
singular perturbation
Mathematics
Subjects
Details
- Language :
- English
- Database :
- OpenAIRE
- Accession number :
- edsair.doi.dedup.....261393e2cfb8c2f44142d27fd8263640