Hermite wavelets operational matrix of integration for the numerical solution of nonlinear singular initial value problems

Shiralashetti, S. C.; Kumbinarasaiah, S.

doi:10.1016/j.aej.2017.07.014

Cited by 80 publications

(46 citation statements)

References 18 publications

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“…Substituting the values of wavelet coefficients into (14), (15) and (16), we obtain the first, second and third derivatives of y.…”

Section: Proposed Scheme For Numerical Differentiationmentioning

confidence: 99%

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Numerical Differentiation via Hermite Wavelets

Singh¹,

Kaur²

2020

Int. J. of Appl. Math.

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“…Substituting the values of wavelet coefficients into (14), (15) and (16), we obtain the first, second and third derivatives of y.…”

Section: Proposed Scheme For Numerical Differentiationmentioning

confidence: 99%

“…Bratu's problem has been solved with the help of Hermite wavelet approach in [12]. Numerical solution of nonlinear singular initial value problems by using operational matrices of integration of Hermite wavelets has been discussed in [14].…”

Section: Introductionmentioning

confidence: 99%

Numerical Differentiation via Hermite Wavelets

Singh¹,

Kaur²

2020

Int. J. of Appl. Math.

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“…Recently, Sunil et al have discussed Bernstein wavelets method for solving SIR epidemic [63]. There are some research articles on Hermite wavelets for solving FDEs [64, 65]. Best of our knowledge, there is not any article based on Hermite wavelets for solving biological models in [0, t l ].…”

Section: Introductionmentioning

confidence: 99%

A fractional model for population dynamics of two interacting species by using spectral and Hermite wavelets methods

Kumar

Ghosh

Kumar

et al. 2020

Numerical Methods Partial

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The Lotka‐Volterra model is a very famous model and frequently used to describe the dynamics of ecological systems in which two species interact, one a predator and one its prey. In this present work, a comparative study is presented for solving Lotka‐Volterra model which has an important role in Biological sciences. The Lotka‐Volterra equations are solved by spectral collocation method (SCM) by using shifted Chebyshev polynomials of first kind. Then, a numerical example with two different cases is presented to demonstrate the accuracy and effectiveness of the numerical schemes. Using spectral method, we get a system of nonlinear algebraic equations which are solved by Newton's iteration method. Also the achieved solutions are compared with another solutions obtained by the Hermite wavelets method (HWM). Further, this work reflects that the integer order Lotka‐Volterra model and the fractional order one have close relationship where integer order model is a special case of fractional order. The behaviors study of predator and prey populations due to presence of fractional derivative are the key features of the present work. Our numerical and graphical results indicate that the proposed methods are simple, powerful and fully compatible for treatment of the Lotka‐Volterra model of fractional order.

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“…Due to this, many authors have found the numerical solution for the diverse class of linear and nonlinear differential and integral equations describing various physical and biological phenomena arisen in daily life using different wavelets based methods. Particularly, Haar wavelet [6,11], Legendre wavelet [27], Laguerre wavelet [24], Hermite wavelet [23] and many others. Among distinct families of wavelets, recently many mathematicians and physicists considered Chebyshev wavelets in order to analyze various model, and proved that the projected wavelets simulates and exemplifies very interesting properties of nonlinear problems in accurate and more efficient manner [22,26].…”

Section: Introductionmentioning

confidence: 99%

Chebyshev wavelets approach for the squeeze film lubrication of long porous journal bearings with couple stress fluids

Shiralashetti¹,

Praveenkumar²

2020

Malaya J. Mat.

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In the present investigation, Chebyshev wavelet-based technique is considered for the study of the effect of couple stress fluid on the squeeze film lubrication in long porous journal bearings. In order to study the pressure distribution, the non-dimensional Reynolds equation is solved by the aid of projected technique. The response of obtained solution with respect to pressure and circumferential coordinate are captured. Further, the physical behaviour of pressure with the help of eccentricity ratio, permeability parameter, and couple stress parameter is analysed and presented in terms of plots. According to results obtained, the couple stress fluid effect significantly increases the pressure as compare to the Newtonian case. Also, when the permeability parameter is decreased and the corresponding pressure decreases as compared to the solid case.

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Hermite wavelets operational matrix of integration for the numerical solution of nonlinear singular initial value problems

Cited by 80 publications

References 18 publications

Numerical Differentiation via Hermite Wavelets

Numerical Differentiation via Hermite Wavelets

A fractional model for population dynamics of two interacting species by using spectral and Hermite wavelets methods

Chebyshev wavelets approach for the squeeze film lubrication of long porous journal bearings with couple stress fluids

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