Scilab/C4/Solving-Non-linear-Equations/English

Title of script: Solving Nonlinear Equations using Numerical Methods

Author: Shamika

Keywords: Nonlinear equation, root, zero

Visual Cue	Narration
Slide 1	Dear Friends, Welcome to the spoken tutorial on “Solving Nonlinear Equations using Numerical Methods”
Slide 2,3 -Objectives	At the end of this tutorial, you will learn how to: Solve nonlinear equations using numerical methods The methods we will be studying are Bisection method and Secant method We will also develop Scilab code to solve nonlinear equations
Slide 4-System Requirements	To record this tutorial, I am using Ubuntu 12.04 as the operating system and Scilab 5.3.3 version
Slide 5- Prerequisites	Before practising this tutorial, a learner should have basic knowledge of Scilab and nonlinear equations For Scilab, please refer to the Scilab tutorials available on the Spoken Tutorial website.
Slide 6	For a given function f , we have to find the value of x for which f of x is equal to zero. This solution x is called root of equation or zero of function f This process is called root finding or zero finding
Slide 7	We begin by studying Bisection Method. In bisection method, we calculate the initial bracket of the root. Then we iterate through the bracket and halve its length. We repeat this proces until we find the solution of the equation.
Slide 8	Let us solve this function using Bisection method Given function f equal to two sin x minus e to the power of x divided by four minus one in the interval minus five and minus three.
Open Bisection.sci on Scilab Editor	* Open Bisection dot sci on Scilab editor Let us look at the code for Bisection method We define the function Bisection with input arguments a b f and tol Here a is the lower limit of the interval b is the upper limit of the interval f is the function to be solved and tol is the tolerance level We specify the maximum number of iterations to be equal to hundred. We find the midpoint of the interval and iterate till the value calculated is within the specified tolerance range.
Click on Execute and select Save and Execute	Let us solve the problem using this code. Save and execute the file
Switch to Scilab console On Scilab Console type, a=-5 Press enter b=-3 Press enter deff('[y]=f(x)','y=(2*(sin(x))-((%e^x)/4)-1') Press enter Tol=10^-5 Press enter Bisection(a,b,f,Tol) Press enter	Switch to Scilab console Let us define the interval. Let a be equal to minus five Press enter Let b be equal to minus three. Press enter Define the function using deff function. We type deff open paranthesis open single quote open square bracket y close square bracket equal to f of x close single quote comma open single quote y equal to two asterisk sin of x minus open paranthesis open paranthesis percentage e to the power of x close paranthesis divided by four close paranthesis minus one close single quote close paranthesis To know more about deff function, type help deff Press enter Let tol be equal to 10 to the power of minus five Press enter To solve the problem, type Bisection open paranthesis a comma b comma f comma tol close paranthesis Press enter The root of the function is shown on the console
Slide 12	Let us study Secant's method. In Secan't method, the derivative is approximated by finite difference using two successive iteration values.
Slide 13	Let us solve this example using Secant method The function is f equal to x square minus six. The two starting guesses are , p zero equal to two and p one equal to three.
Open Secant.sci on Scilab Editor	Before we solve the problem, let us look at the code for Secant meethod. Open Secant dot sci on Scilab editor We define the function secant with input arguments a, b and f a is first starting guess for the root b is the second starting guess and f is the function to be solved. We find the difference between the value at the current point and the previous point. We apply Secant's method and find the value of the root. Finally we end the function
Click on Execute and select Save and Execute	Let me save and execute the code.
Switch to Scilab console Type on Scilab console clc Press enter a=2 Press enter b=3 Press enter deff('[y]=g(x)','y=(x^2)-6') Press enter Secant(a,b,g) Press enter	Switch to Scilab console Type clc Press enter Let me define the initial guesses for this example. Type a equal to 2 Press enter Then type b equal to 3 Press enter We define the function using deff function. Type deff open paranthesis open single quote open square bracket y close square bracket equal to g of x close single quote comma open single quote y equal to open paranthesis x to the power of two close paranthesis minus six close single quote close paranthesis Press enter We call the function by typing Secant open paranthesis a comma b comma g close paranthesis. Press enter The value of the root is shown on the console
Slide 14	Let us summarize this tutorial In this tutorial we have learnt to: Find the roots of nonlinear equation Develop Scilab code for different solving methods
Slide 15- Assignment	Solve this problem on your own using the two methods we learnt today.
Show Slide 16 Title: About the Spoken Tutorial Project Watch the video available at http://spoken-tutorial.org/What_is_a_Spoken_Tutorial It summarises the Spoken Tutorial project If you do not have good bandwidth, you can download and watch it	* Watch the video available at the following link It summarises the Spoken Tutorial project If you do not have good bandwidth, you can download and watch it
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Show Slide 18 Title: Acknowledgement Spoken Tutorial Project is a part of the Talk to a Teacher project It is supported by the National Mission on Education through ICT, MHRD, Government of India More information on this Mission is available at http://spoken-tutorial.org/NMEICT-Intro	* Spoken Tutorial Project is a part of the Talk to a Teacher project It is supported by the National Mission on Education through ICT, MHRD, Government of India More information on this Mission is available at spoken hyphen tutorial dot org slash NMEICT hyphen Intro
On previous slide	This is Ashwini Patil signing off. Thanks for joining.

Contributors and Content Editors

Lavitha Pereira, Nancyvarkey