Solutions of nonlinear systems by reproducing kernel method

Abstract

A novel approximate solution is obtained for viscoelastic fluid model by reproducing kernel method (RKM). The resulting equation for viscoelastic fluid with magneto-hydrodynamic flow is transformed to the nonlinear system by introducing the dimensionless variables. Results are presented graphically to study the efficiency and accuracy of the reproducing kernel method. Results show that this method namely RKM is an efficient method for solving nonlinear system in any engineering field.

On the Matlab Technique by Using Laplace Transform for Solving Second Order Ode With Initial Conditions Exactly

“…A transformations method can be used to get an exact solution to a differential equation. There are many methods which use transformation, Laplace transforms are commonly used in solving mathematical and physical problems which contains ordinary or partial differential equations with constant coefficients and integral equations as those problems are arising in the many branches of physics as electronic circuit analysis [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15]. But it takes too much time for solving by hand and in papers, These ODE can be analyzed.…”

Lomax Weibull Distribution

“…Due to its advantage in modelling lifetime data as compared to the other distributions, many researchers continue to develop modified versions of the general Weibull distribution with the aim of increasing its flexibility [4,5,6,7,8,9,10,[11][12][13][14][15]. An extensive review of modifications of the Weibull distribution together with expressions for the CDFs, PMF, or the PDF as well as the hazard functions was presented by [16].…”

An efficient method for solving fractional Ricatti equations

“…For example, see [5][6][7]. Akgul, et al, discussed several fractional problems using different methods such as the reproducing kernel Hilbert space method [8][9][10][11][12][13][14][15][16], while Alquran, et al, used a fractional power series method [17][18][19][20][21][22][23][24]. In this article, we consider the following class of equations:…”