This document discusses using the Newton Raphson method in MATLAB to find the roots of nonlinear equations. It begins with an introduction to the Newton Raphson method and its use in solving equations that are too complex for algebraic methods. The objectives and theory behind the Newton Raphson method are then outlined. Examples are provided and the MATLAB code presented to find the roots of sample equations graphically and via the console output. The document walks through applying the Newton Raphson method in MATLAB to several equations.

1. IT-2210 : Computational
mathematics LAB with
MATLAB
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2. Lecture 6: MATLAB – Newton Raphson
method.
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Newton Raphson method
In scientific and engineering work, a frequently
occurring problem is to find the roots of equations of
the form y = f(x) = 0, i.e finding the value of x where
the value of y = f(x) is equal to 0. In quadratic, cubic
or a biquadratic equations, algebraic formulae are
available for expressing the roots in terms of co-
efficient. But in the case, where f(x) is a polynomial of
higher degree or an expression involving
transcendental functions, the algebraic methods are not
applicable and the help of numerical method must be
taken to find approximate roots.

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Objectives of this experiment
• To write a program in order to find out the real
roots of a nonlinear equation by Newton
Raphson Method.

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Theory

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Theory Cont……

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Theory Cont……

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Theory Cont……

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Example 1 of N-R method

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Example 1 of N-R method cont…

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MATLAB code for
Newton Raphson
method

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MATLAB output for
Newton Raphson
method
For the equation: f(x) = cos(x)-3*x+1

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MATLAB output of N-R method (Graph)

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MATLAB output of N-R method (Console)
For the equation: f(x) = cos(x)-3*x+1

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Now solve with MATLAB and show the output in console and Graph
1. f(x) = 2*x^3 - 3*x -6
2. f(x) = x^3 – 6*x + 4
3. 3x-cosx-1=0
4. cos𝑥−𝑥𝑒𝑥=0

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MATLAB output of N-R method (Graph)
For the equation: f(x) = 2*x^3 - 3*x -6

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MATLAB output of N-R method (Console)
For the equation: f(x) = 2*x^3 - 3*x -6

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Output for
f(x) = x^3 – 6*x + 4

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End of
LECTURE six
Thank You .
References: MSK and MMS sir’s
lecture.