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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.
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.
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.
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.
M. Govarthanan,R. Mythili,T. Selvankumar,카말라칸,최두복,장영철 한국생물공학회 2017 Biotechnology and Bioprocess Engineering Vol.22 No.2
Objective of the study was to isolate heavy metal resistant bacteria from chromium-contaminated subsurface soil and investigate biosurfactant production and heavy metal bioremediation. Based on 16S rRNA gene sequence and phylogenetic analysis, the isolate was identified as Rahnella sp. RM. The biosurfactant production by heavy metal resistant Rahnella sp. RM was optimized using Box- Behnken design (BBD). The maximum emulsification activity was obtained 66% at 6% soybean meal in pH 7.0 and 33.5°C. The biosurfactant was characterized using Field emission scanning electron microscopy (FE-SEM), Fourier transform infrared spectroscopy (FT-IR) and matrix assisted laser desorption/ionization time of flight mass spectrometry (MALDI-TOF). The highest metal removal rates using the biosurfactant were found 74.3, 72.5, and 70.1%, respectively, at the 100 mg/L amended flasks at 48 h. This study indicated the biosurfactant from heavy metal resistant Rahnella sp. RM could be used as a potential tool to remediate the metals in contaminated environments.
Singh Akash,Thirumurugesan R.,Krishnakumar S.,Rani Revati,Chandramouli S.,Parameswaran P.,Mythili R. 한국원자력학회 2023 Nuclear Engineering and Technology Vol.55 No.4
Enhancement of wear resistance of components used in fast reactors is necessary for long service life of the components. Plasma nitriding is a promising surface modification technology to impart high hardness and improved wear resistance of various steel components. This study discusses the characterization of chrome nitrided SS316L casing ring used in secondary sodium pump of fast breeder reactor and its stability under long term sodium exposure. Microstructural and hardness analysis showed that stress relieved component could be chrome nitrided successfully to a thickness of about 100 μm. Assessment of in-sodium performance of the chrome nitrided casing ring subjected to long term exposure up to 5000h at 550°C, showed retention of chrome nitrided layer with a case depth almost similar to that before sodium exposure. A slight decrease in the hardness was observed due to prolonged high temperature sodium exposure. Tribological studies indicate very low coefficient of friction indicating the retention of good wear resistance of the coating even after long term sodium exposure.
A. Tamilselvan,N. Ramanujam,R. Mythili Priyadharshini,T. Valanarasu 한국전산응용수학회 2010 Journal of applied mathematics & informatics Vol.28 No.1
In this paper, a numerical method for a weakly coupled system of two singularly perturbed convection-diffusion second order ordinary differential equations with the mixed type boundary conditions is presented. Parameter-uniform error bounds for the numerical solution and also to numerical derivative are established. Numerical results are provided to illustrate the theoretical results.