Applications The knowledge of mathematics is frequently applied through word problems and the applications of linear equations are observed on a wide scale to solve such word problems.
The main purpose of this technique is to resolve linear and nonlinear problems by using of differential transform method. We get the approximate solution with the help of differential transformation method DTMand also catch the quickly convergent series.
Comparisons with exact solution show that the DTM is a most dominant method to catch the exact solution of nonlinear Ordinary differential equations. The differential equations which can show very complicated behavior over long time intervals, is the non-linear differential equation.
Even the major questions Essay on linear equations existence, uniqueness, and extendibility of solutions for nonlinear differential equations, and well-posedness of initial and boundary value problems for nonlinear ordinary differential equations ODEs and partial differential equations PDEs are tough problems and their purpose in special cases is considered to be a forceful advance in the mathematical theory.
The set of simultaneous equations in which the unknowns appear as variables of a polynomial of degree higher than one or in the argument of a function which is not a polynomial of degree one is called the non-linear set of equations.
The nature of a nonlinear system is defined by a nonlinear system of equations. Nonlinear problems are of interest to engineers, physicists and mathematicians and many other scientists because most systems are characteristically nonlinear in nature.
Non-linear differential equations are solved by few methods to find the exact solution. Many effective methods have been proposed for finding the analytical solutions. These methods provide immediate and visible symbolic terms of analytic solutions, as well as numerical approximate solutions of differential equations.
The analytical method for solving differential equations is the differential transformation method.
The idea of differential transform was first introduced by Zhouwho was the first one to use differential transform method DTM in engineering applications. He applied DTM in solution of initial boundary value problems for the analysis of electric circuit. In recent years, theory of DTM has extended to the problems involving Ordinary differential equations and systems of differential equations.
This method makes an analytical solution in the form of polynomial. This method avoids the large computation values and rounding off error, it gives exact analytical solution. Is it Differential transformation Method always effective and gives consistent solution for non-linear problems and systems?
It will be confirmed about the reliability and efficiency of proposed method. The Differential transform method is the indications of an iterative process for obtaining an analytic series solutions of functional equations. In most recent years researchers have practically apply the method to various linear and nonlinear problems such as two point boundary value problems by Chen and Liu , partial differential equations by Jang et al.
This method provides analytical convergent solution. In the first chapter, we shall give some preliminaries and analysis of the DTM and literature review of application of proposed method 8. Essay UK - http:Linear equation & Matrices Essay Sample. Linear equation is an equations are equations between two variables that make a straight line when it is graphed.
Free practice questions for SAT Math - Systems of Equations. Includes full solutions and score reporting. Different Forms. There are many ways of writing linear equations, but they usually have constants (like "2" or "c") and must have simple variables (like "x" or "y").
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