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Numerical solution of singularly perturbed two parameter problems using exponential splines

Padmaja P., Aparna P., Gorla Rama Subba Reddy, Pothanna N.

International Journal of Applied Mechanics and Engineering

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2021

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Vol. 26, no. 2

160--172

EN

In this paper, we have studied a method based on exponential splines for numerical solution of singularly perturbed two parameter boundary value problems. The boundary value problem is solved on a Shishkin mesh by using exponential splines. Numerical results are tabulated for different values of the perturbation parameters. From the numerical results, it is found that the method approximates the exact solution very well.

2

An intial-value technique for self-adjoint singularly perturbed two-point boundary value problems

Padmaja P., Aparna P., Gorla R. S. R.

International Journal of Applied Mechanics and Engineering

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2020

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Vol. 25, no. 1

106--126

EN

In this paper, we present an initial value technique for solving self-adjoint singularly perturbed linearvboundary value problems. The original problem is reduced to its normal form and the reduced problem is converted to first order initial value problems. This replacement is significant from the computational point of view. The classical fourth order Runge-Kutta method is used to solve these initial value problems. This approach to solve singularly perturbed boundary-value problems is numerically very appealing. To demonstrate the applicability of this method, we have applied it on several linear examples with left-end boundary layer and rightend layer. From the numerical results, the method seems accurate and solutions to problems with extremely thin boundary layers are obtained.

3

A numerical study of coupled non-linear equations of thermo-viscous fluid flow in cylindrical geometry

Pothanna N., Aparna P., Gorla R. S. R.

International Journal of Applied Mechanics and Engineering

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2017

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Vol. 22, no. 4

965--979

EN

In this paper we present numerical solutions to coupled non-linear governing equations of thermo-viscous fluid flow in cylindrical geometry using MATHEMATICA software solver. The numerical results are presented in terms of velocity, temperature and pressure distribution for various values of the material parameters such as the thermo-mechanical stress coefficient, thermal conductivity coefficient, Reiner Rivlin cross viscosity coefficient and the Prandtl number in the form of tables and graphs. Also, the solutions to governing equations for slow steady motion of a fluid have been obtained numerically and compared with the existing analytical results and are found to be in excellent agreement. The results of the present study will hopefully enable a better understanding applications of the flow under consideration.

4

Analysis and comparison of symmetry based lossless and perceptually lossless algorithms for volumetric compression of medical images

Chandrika B. K., Aparna P., Sumam D. S.

Journal of Medical Informatics & Technologies

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2015

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Vol. 24

147--154

EN

Modern medical imaging techniques produce huge volume of data from stack of images generated in a single examination. To compress them several volumetric compression techniques have been proposed. Performance of these compression schemes can be improved further by considering the anatomical symmetry present in medical images and incorporating the characteristics of human visual system. In this paper a volumetric medical image compression algorithm is presented in which perceptual model is integrated with a symmetry based lossless scheme. Symmetry based lossless and perceptually lossless algorithms were evaluated on a set of three dimensional medical images. Experimental results show that symmetry based perceptually lossless coder gives an average of 8.47% improvement in bit per pixel without any perceivable degradation in visual quality against the lossless scheme.