differential equation by b.d. sharma pdf 333

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In this class, an Ordinary differential equation will be discussed. In mathematics, an 
ordinary differential equation
 (
ODE
) is a differential equation containing one or more functions of one independent variable and the derivatives of those functions. The term ordinary is used in contrast with the term partial differential equation which may be with respect to more than one independent variable.


In this paper, we built the KHDE with future event horizon as IR cutoff in a non-flat universe with model parameters 
K
 and 
c
. KHDE is constructed by applying Kaniadakis entropy to a cosmological framework instead of normal Bekenstein Hawking entropy and the holographic principle. We first offered a straightforward differential equation for the holographic dark energy density parameter \(\Omega _d\) in order to examine the cosmic applications of KHDE. Additionally, as a function of \(\Omega _d\), we deduced an analytical expression for the holographic dark energy equation-of-state parameter \(w_d\) while accounting for both closed and open spatial geometry. Although the aforementioned differential equation can be analytically solved in an implicit form when \(K=0\) and \(\gamma =0\), in general case it can not be solved analytically, hence one must numerically elaborate it.


Download PDF Download. Export . the fractional nonlinear SharmaTassoOlver equation has been studied by several . into an ordinary differential equation and .CHAPTER 12 Second Order Linear Differential Equations 12.1. Homogeneous Equations A differential equation is a relation involvingvariables x y y y .The Fokker-Planck equation 3 1.Chapter 2 Ordinary Differential Equations Chapter 2 Ordinary Differential Equations 2.1 Basic concepts, definitions, notations and classification Introduction modeling in engineeringAbstract. This work deals with the existence of solutions for a class of nonlinear nonlocal fractional functional differential equations of neutral type in Banach spaces. e31cf57bcd


This paper introduces a new algorithm for solving ordinary differential equations (ODEs) with initial or boundary conditions. In our proposed method, the trial solution of differential equation has been used in the regression-based neural network (RBNN) model for single input and single output system. The artificial neural network (ANN) trial solution of ODE is written as sum of two terms, first one satisfies initial/boundary conditions and contains no adjustable parameters. The second part involves a RBNN model containing adjustable parameters. Network has been trained using the initial weights generated by the coefficients of regression fitting. We have used feed-forward neural network and error back propagation algorithm for minimizing error function. Proposed model has been tested for first, second and fourth-order ODEs. We also compare the results of proposed algorithm with the traditional ANN algorithm. The idea may very well be extended to other complicated differential equations.


The purpose of the present study is to solve partial differential equations (PDEs) using single layer functional link artificial neural network method. Numerical solution of elliptic PDEs have been obtained here by applying Chebyshev neural network (...
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Differential Equation By B.d. Sharma Pdf 333

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