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Uploaded byTajim Md. Niamat Ullah Akhund
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Matlab lecture 6 – newton raphson method@taj copy

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.

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IT-2210 : Computational mathematics LAB with MATLAB 4/10/2017MATLAB by Tajim 1
Lecture 6: MATLAB – Newton Raphson method. 4/10/2017MATLAB by Tajim 2
4/10/2017MATLAB by Tajim 3 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.
4/10/2017MATLAB by Tajim 4 Objectives of this experiment • To write a program in order to find out the real roots of a nonlinear equation by Newton Raphson Method.
4/10/2017MATLAB by Tajim 5 Theory
4/10/2017MATLAB by Tajim 6 Theory Cont……
4/10/2017MATLAB by Tajim 7 Theory Cont……
4/10/2017MATLAB by Tajim 8 Theory Cont……
4/10/2017MATLAB by Tajim 9 Example 1 of N-R method
4/10/2017MATLAB by Tajim 10 Example 1 of N-R method cont…
4/10/2017MATLAB by Tajim 11 MATLAB code for Newton Raphson method
4/10/2017MATLAB by Tajim 12
4/10/2017MATLAB by Tajim 13 MATLAB output for Newton Raphson method For the equation: f(x) = cos(x)-3*x+1
4/10/2017MATLAB by Tajim 14 MATLAB output of N-R method (Graph)
4/10/2017MATLAB by Tajim 15 MATLAB output of N-R method (Console) For the equation: f(x) = cos(x)-3*x+1
4/10/2017MATLAB by Tajim 16 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
4/10/2017MATLAB by Tajim 17 MATLAB output of N-R method (Graph) For the equation: f(x) = 2*x^3 - 3*x -6
4/10/2017MATLAB by Tajim 18 MATLAB output of N-R method (Console) For the equation: f(x) = 2*x^3 - 3*x -6
4/10/2017MATLAB by Tajim 19 Output for f(x) = x^3 – 6*x + 4
4/10/2017MATLAB by Tajim 20 End of LECTURE six Thank You . References: MSK and MMS sir’s lecture.