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6 results on '"Vimal Vikash"'

1. An unconditionally stable numerical scheme for solving nonlinear Fisher equation

Author

Vimal Vikash, Sinha Rajesh Kumar, and Liju Pannikkal

Subjects
fisher equation, finite differences, backward differentiation formula, method of line, newton method, Engineering (General). Civil engineering (General), TA1-2040
Abstract

In this study, novel numerical methods are presented for solving nonlinear Fisher equations. These equations have a wide range of applications in various scientific and engineering fields, particularly in the biomedical sciences for determining the size of brain tumors. The challenges posed by the nonlinearity of the equations are effectively addressed through the development of numerical techniques. The nonlinearity is tackled using a combination of the method of lines and backward differentiation formulas of varied orders. This method is unconditionally stable, and its accuracy is evaluated using error norms. The methods are successfully validated against test problems with known solutions, demonstrating their superiority through comparative analyses with existing methodologies in the literature.

Published
2024
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2. BACKWARD DIFFERENTIATION FORMULA BASED NUMERICAL METHOD TO SOLVE FISHER EQUATION.

Author

Vimal, Vikash, Sinha, Rajesh Kumar, and P., Liju

Subjects
ORDINARY differential equations, EQUATIONS, ENGINEERING
Abstract

This paper presents a novel numerical approach, which is based on the Method of Lines. This method semi-discretizes the problem and produces a system of ordinary differential equations (ODEs) in time. To solve this system, a stiff solver, BDF2, is used, which yields very precise results. The linearization is handled by the Taylor series method. To validate the numerical method, various test examples are considered. These formulas find extensive applications across various scientific and engineering domains. [ABSTRACT FROM AUTHOR]

Published
2024
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4. A numerical implementation of higher-order time integration method for the transient heat conduction equation with a moving boundary based on boundary immobilization technique.

Author

Parambu, Rabeeb Ali Valiyakam, Awasthi, Ashish, Vimal, Vikash, Jha, Naveen, John, Sunil Jacob, and Panda, Satyananda

Subjects
HEAT conduction, HEAT equation, FINITE differences, THERAPEUTIC immobilization, RUNGE-Kutta formulas
Abstract

In this paper, we are proposing an efficient method to solve the transient heat conduction equation with a moving boundary based on the boundary immobilization method (BIM). The transformed problem is semi discretized by the method of lines (MOL), i.e., central finite difference approximation is made for the spatial derivatives. The resultant system of ordinary differential equations applied the strong stability preserving Runge-Kutta methods (SSP-RK43). A transient heat conduction equation with a moving boundary having exact solutions is considered to check the efficiency and accuracy of the numerical schemes. l2 and l∞ error norms are taken to compare numerical results with the corresponding exact solution. [ABSTRACT FROM AUTHOR]

Published
2020
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5. Gene masking - a technique to improve accuracy for cancer classification with high dimensionality in microarray data

Author

Tatsuhiko Tsunoda, Harsh Saini, Gurmeet Singh, Vincel Wince Pickering, Alok Sharma, Sunil Pranit Lal, and Vimal Vikash Naidu

Subjects
0301 basic medicine, Masking (art), Cancer classification, Feature vector, Binary number, Feature selection, 02 engineering and technology, Biology, Bioinformatics, 03 medical and health sciences, Neoplasms, Genetic algorithm, 0202 electrical engineering, electronic engineering, information engineering, Genetics, Humans, Genetics(clinical), Child, Genetics (clinical), Oligonucleotide Array Sequence Analysis, Microarray analysis techniques, business.industry, Research, Pattern recognition, 030104 developmental biology, ComputingMethodologies_PATTERNRECOGNITION, Genetic Techniques, 020201 artificial intelligence & image processing, Artificial intelligence, High dimensionality, business, Algorithms
Abstract

Background High dimensional feature space generally degrades classification in several applications. In this paper, we propose a strategy called gene masking, in which non-contributing dimensions are heuristically removed from the data to improve classification accuracy. Methods Gene masking is implemented via a binary encoded genetic algorithm that can be integrated seamlessly with classifiers during the training phase of classification to perform feature selection. It can also be used to discriminate between features that contribute most to the classification, thereby, allowing researchers to isolate features that may have special significance. Results This technique was applied on publicly available datasets whereby it substantially reduced the number of features used for classification while maintaining high accuracies. Conclusion The proposed technique can be extremely useful in feature selection as it heuristically removes non-contributing features to improve the performance of classifiers.

Published
2016

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