Abstract
This work focuses on nonlinear equation (x) = 0, it is noted that no or little attention is given to nonlinear equations. The purpose of this work is to determine the best method of solving nonlinear equations. The work outlined four methods of solving nonlinear equations. Unlike linear equations, most nonlinear equations cannot be solved in finite number of steps. Iterative methods are being used to solve nonlinear equations. The cost of solving nonlinear equations problems depend on both the cost per iteration and the number of iterations required. Derivations of each of the methods were obtained. An example was illustrated to show the results of all the four methods and the results were collected, tabulated and analyzed in terms of their errors and convergence respectively. The results were also presented in form of graphs. The implication is that the higher the rate of convergence determines how fast it will get to the approximate root or solution of the equation. Thus, it was recommended that the Newton’s method is the best method of solving the nonlinear equation f(x) = 0 containing one variable because of its high rate of convergence.
Highlights
Numerical methods are used to provide constructive solutions to problems involving nonlinear equations
The study of this work cannot be discussed at peak without first making necessary attempts to discuss the branch of mathematics that it arises from which is numerical analysis
Following the example f ( x) = x3 + x −1 of the nonlinear equation and illustrating the results by the four methods of solving nonlinear equations f(x)= 0 in this work, the results of the methods are presented in the graphs and table below
Summary
Numerical methods are used to provide constructive solutions to problems involving nonlinear equations. Okorie Charity Ebelechukwu et al.: Comparison of Some Iterative Methods of Solving Nonlinear Equations involving more complicated terms such as trigonometric, hyperbolic, exponential or logarithmic functions are referred to as transcendental equations. This in general is referred as nonlinear equations. [5] It is well known that when the Jacobian of nonlinear systems is nonsingular in the neighborhood of the solution, the convergence of Newton method is guaranteed and the rate is quadratic. The solution is not exact when the coefficient is numerical values, it can adopt various numerical approximate methods to solve such algebraic and transcendental equations. Numerical methods like Newton’s method are often used to obtain the approximate solution of such problems because it is not always possible to obtain its exact solution by usual algebraic process [8]
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