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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.
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.
Suganya Priyadharshini G.,Subramanian R.,Murugan N.,Sathiskumar R. 대한기계학회 2017 JOURNAL OF MECHANICAL SCIENCE AND TECHNOLOGY Vol.31 No.8
In the present research work, Friction stir processing (FSP) technique has been applied to develop a C70600 graded copper-nickel (CuNi) Surface metal matrix composite (SMMC) reinforced with and without addition of ZrCp. Rotational and traverse speeds were set as 1200 rpm and 30 mm/min, respectively. The fabricated SMMC were metallurgically characterized by using Optical microscope (OM) and Field emission scanning electron microscope (FESEM). The homogeneous distribution of ZrC particles and good interfacial bonding between matrix/reinforcement were observed via OM and FESEM microscopes. The microhardness of the CuNi/ZrC surface composite was observed by using microhardness tester at the cross section of the sample. The average higher microhardness of 148 Hv at CuNi/ZrC SMMC and lower microhardness of 115 Hv at FSPed CuNi was found. The Ultimate tensile strength (UTS) value was measured by using micro tensile testing machine. The UTS value of CuNi/ZrC composite and FSPed CuNi were observed to be 310 MPa and 302 MPa, respectively. The mode of fracture was also observed via FESEM. The X-ray diffraction (XRD) test was carried out to confirm the presence of CuNi & ZrC in the SMMC layer.
R. Ponalagusamy,S. Priyadharshini 한국유변학회 2017 Korea-Australia rheology journal Vol.29 No.4
The present study investigates the pulsatile flow of Casson nanofluid through an inclined and stenosed artery with tapering in the presence of magnetic field and periodic body acceleration. The iron oxide nanoparticles are allowed to flow along with it. The governing equations for the flow of Casson fluid when the artery is tapered slightly having mild stenosis are highly non-linear and the momentum equations for temperature and concentration are coupled and are solved using finite difference numerical schemes in order to find the solutions for velocity, temperature, concentration, wall shear stress, and resistance to blood flow. The aim of the present study is to analyze the effects of flow parameters on the flow of nanofluid through an inclined arterial stenosis with tapering. These effects are represented graphically and concluded that the wall shear stress profiles enhance with increase in yield stress, magnetic field, thermophoresis parameter and decreases with Brownian motion parameter, local temperature Grashof number, local nanoparticle Grashof number. The significance of the model is the existence of yield stress and it is examined that when the rheology of blood changes from Newtonian to Casson fluid, the percentage of decrease in the flow resistance is higher with respect to the increase in the parameters local temperature Grashof number, local nanoparticle Grashof number, Brownian motion parameter, and Prandtl number. It is pertinent to observe that increase in the Brownian motion parameter leads to increment in concentration and temperature profiles. It is observed that the concentration of nanoparticles decreases with increase in the value of thermophoresis parameter.
Development of Symmetrical Fault Detection During Power Swing Based on Entropy
Devi R.,Kirthika A.,Divya Priyadharshini M.,Ladha Akash,Anju A.,Rajesh Kumar T.,Ganesh Prabhu S.,Varghese Lijo Jacob,Santhosh P. 대한전기학회 2022 Journal of Electrical Engineering & Technology Vol.17 No.3
This paper proposes the new technique for detecting symmetrical faults occurred during power swing. The proposed technique is simulated for the protection of two machine system, distribution system with distributed generation and WSCC 9-bus system in Matlab. Symmetrical fault detection during power swing is a critical issue. Hence, in this paper, modifi ed weighted wavelet packet entropy technique is proposed to detect symmetrical fault during power swing. This entropy criterion is applied to wavelet packet coeffi cients to enhance the energy of fault signals and to reduce the vector size of the wavelet packet transform coeffi cients. This technique provides better results irrespective of various fault locations, fault inception angle and power swing frequencies. This technique is compared with conventional scheme and the results are tabulated. Moreover, this technique is also able to detect asymmetrical faults with high impedance during power swing. Mathematical derivation support system performance through simulation.
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.