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.
In this paper, the CAS wavelets stochastic operational matrix method is developed for the numerical solution of stochastic integral equations. Properties of CAS wavelets and its function approximation are discussed. Firstly, the CAS wavelets stochastic operational matrix of integration is generated. This stochastic operational matrix is employed for solving stochastic integral equations. Next, this technique converts the stochastic integral equation into system of algebraic equations and then solving these equations we obtain the CAS wavelet coefficients. The accuracy of the proposed method is justified through the Illustrative example and the obtained solutions are compared with those of exact solutions. Error analysis is presented to show the efficiency of the proposed method.
Many physical problems when analysed assumes the form of a partial differential equations. Recently wavelet transforms serves as a very useful tool in solving partial differential equations. In this paper, we proposed an efficient numerical scheme based on Euler wavelets for the solutions of parabolic partial differential equations. Some Illustrative examples are included to demonstrate the validity and applicability of the proposed scheme. Numerical findings of the problems with both initial and boundary conditions shows the efficiency and accuracy of the present scheme.
In this paper, the numerical solution of the system of ordinary differential equations by Haar wavelet method is presented. The interest is on solving the problem using the Haar wavelet basis due to its simplicity and efficiency in numerical approximations. The approach of Haar wavelet method for the numerical solution of system of equations is mentioned and the obtained numerical solution has been compared with exact solution. Also, the numerical results are presented for demonstrating the validity and applicability of the Haar wavelet method.
In this article, we are going to use Hermite wavelet method and here we are proposed scheme for the numerical results of nonlinear singular initial value problems. presently, series of derivatives is come into picture by using Hermite wavelets. With the help of these derivatives, proposed method is developed.Properties of Hermite wavelets are used to convert nonlinear singular initial value problems with initial conditions and collocation points to systems of nonlinear algebraic equations. And then this system of equations can be solved by using suitable methods. Some of the numerical test problems are given to express the validity and the accuracy of the proposed method.
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