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Hybrid difference schemes for a system of singularly perturbed convection-diffusion equations
R. Mythili Priyadharshini,N. Ramanujam,A. Tamilselvan 한국전산응용수학회 2009 Journal of applied mathematics & informatics Vol.27 No.5
In this paper, two hybrid difference schemes on the Shishkin mesh are constructed for solving a weakly coupled system of two singularly perturbed convection-diffusion second order ordinary differential equations with a small parameter multiplying the highest derivative. We prove that the schemes are almost second order convergence in the supremum norm independent of the diffusion parameter. Error bounds for the numerical solution and its derivative are established. Numerical results are provided to illustrate the theoretical results. In this paper, two hybrid difference schemes on the Shishkin mesh are constructed for solving a weakly coupled system of two singularly perturbed convection-diffusion second order ordinary differential equations with a small parameter multiplying the highest derivative. We prove that the schemes are almost second order convergence in the supremum norm independent of the diffusion parameter. Error bounds for the numerical solution and its derivative are established. Numerical results are provided to illustrate the theoretical results.
R. Mythili Priyadharshini,N. Ramanujam 한국전산응용수학회 2009 Journal of applied mathematics & informatics Vol.27 No.3
In this paper, a singularly perturbed reaction-convection-diffusion problem with two parameters is considered. A parameter -uniform error bound for the numerical derivative is derived. The numerical method considered here is a standard finite difference scheme on piecewise-uniform Shishkin mesh, which is fitted to both boundary and initial layers. Numerical results are provided to illustrate the theoretical results. In this paper, a singularly perturbed reaction-convection-diffusion problem with two parameters is considered. A parameter -uniform error bound for the numerical derivative is derived. The numerical method considered here is a standard finite difference scheme on piecewise-uniform Shishkin mesh, which is fitted to both boundary and initial layers. Numerical results are provided to illustrate the theoretical results.
HYBRID DIFFERENCE SCHEMES FOR A SYSTEM OF SINGULARLY PERTURBED CONVECTION-DIFFUSION EQUATIONS
Priyadharshini, R.Mythili,Ramanujam, N.,Tamilselvan, A. The Korean Society for Computational and Applied M 2009 Journal of applied mathematics & informatics Vol.27 No.5
In this paper, two hybrid difference schemes on the Shishkin mesh are constructed for solving a weakly coupled system of two singularly perturbed convection-diffusion second order ordinary differential equations with a small parameter multiplying the highest derivative. We prove that the schemes are almost second order convergence in the supremum norm independent of the diffusion parameter. Error bounds for the numerical solution and its derivative are established. Numerical results are provided to illustrate the theoretical results.
Priyadharshini, R. Mythili,Ramanujam, N.,Valanarasu, T. The Korean Society for Computational and Applied M 2010 Journal of applied mathematics & informatics Vol.28 No.5
We consider a mixed type singularly perturbed one dimensional elliptic problem with discontinuous source term. The domain under consideration is partitioned into two subdomains. A convection-diffusion and a reaction-diffusion type equations are posed on the first and second subdomains respectively. Two hybrid difference schemes on Shishkin mesh are constructed and we prove that the schemes are almost second order convergence in the maximum norm independent of the diffusion parameter. Error bounds for the numerical solution and its numerical derivative are established. Numerical results are presented which support the theoretical results.
Priyadharshini, R. Mythili,Ramanujam, N. The Korean Society for Computational and Applied M 2009 Journal of applied mathematics & informatics Vol.27 No.3
In this paper, a singularly perturbed reaction-convection-diffusion problem with two parameters is considered. A parameter-uniform error bound for the numerical derivative is derived. The numerical method considered here is a standard finite difference scheme on piecewise-uniform Shishkin mesh, which is fitted to both boundary and initial layers. Numerical results are provided to illustrate the theoretical results.
N. Ramanujam,R. Mythili Priyadharshini,T. Valanarasu 한국전산응용수학회 2010 Journal of applied mathematics & informatics Vol.28 No.5
We consider a mixed type singularly perturbed one dimensional elliptic problem with discontinuous source term. The domain under consideration is partitioned into two subdomains. A convection-diffusion and a reaction-diffusion type equations are posed on the first and second subdomains respectively. Two hybrid difference schemes on Shishkin mesh are constructed and we prove that the schemes are almost second order convergence in the maximum norm independent of the diffusion parameter. Error bounds for the numerical solution and its numerical derivative are established. Numerical results are presented which support the theoretical results.