Description

Lab Assignment 7
Student and ID : Pushkar Patel (201851094)

1 Consider the nonlinear equations
1.1 f(x) = 2.0 – x + ln(x) = 0
1.2 f(x) = x2 – 3x + 1 = 0
Write a MATLAB function to solve the non-linear equations using Bisection method, Fixed point iteration method, Newton-Raphson method. Use fzero() and fsolve() MATLAB functions to verify your answers.
1
Matlab script to calculate solving nonlinear equation f(x) = 2.0-x + ln(x) = 0
Table of Contents
………………………………………………………………………………………………………………………. 1
Function Calling ………………………………………………………………………………………………….. 1 Bisection Method …………………………………………………………………………………………………. 1 Fixed Point Iterator; ……………………………………………………………………………………………… 2 NEWTON METHOD ……………………………………………………………………………………………. 3
clc; clear; close all;
Function Calling
bisecting() fpt() newton()
Bisection Method
function bisecting() x1=1.0; x2=5.0; f1=finder(1,x1); f2=finder(1,x2); maxitr=50; tol=10^-6; if(f1*f2>0)
fprintf(“Invalid guess !!”); end err=zeros(1,maxitr);
for itr=1:1:maxitr m=(x1+x2)/2; fm=finder(1,m); err(itr)=abs(f2-f1); if(err(itr)<tol) break end if(f1*fm>0) x1=m;
f1=fm; else x2=m; f2=fm; end
end m figure(1) plot(err(1:itr-1),err(2:itr)) title(‘plot for bisection method’) end
m = 3.1462

Fixed Point Iterator;
function fpt() x=4; xold=4; maxitr=50; errfp=zeros(1,maxitr);

tol=10^-6;
for itr=1:1:maxitr x=finder(2,xold); errfp(itr)=abs(x-xold); xold=x; if errfp(itr)<tol break end end x figure(2) plot(errfp(1:itr-1),errfp(2:itr)) title(‘plot for ftp method’) end
x = 3.1462

NEWTON METHOD
function newton() x=4;
maxitr=50; errnt=zeros(1,maxitr); tol=10^-6;
for itr=1:1:maxitr fx=finder(1,x); dfx=finder(3,x); xnew=x-fx/dfx; errnt(itr)=abs(xnew-x); if(errnt(itr)<tol) break end x=xnew;
end xnew figure(3) plot(errnt(1:itr-1),errnt(2:itr)) title(‘plot for newton method’) end function fval=finder(arg,xval) if arg==1 fval=2-xval+log(xval); elseif arg==2 fval=2+log(xval); else fval=1/(xval)-1; end end
xnew = 3.1462

Published with MATLAB® R2019b

Matlab script to calculate solving nonlinear equation f(x) = x^2 – 3x + 1 = 0
Table of Contents
………………………………………………………………………………………………………………………. 1
Function Calling ………………………………………………………………………………………………….. 1 Bisection Method …………………………………………………………………………………………………. 1 Fixed Point Iterator; ……………………………………………………………………………………………… 2 NEWTON METHOD ……………………………………………………………………………………………. 3
clc; clear; close all;
Function Calling
bisecting() fpt() newton()
Bisection Method
function bisecting() x1=2.0; x2=4.0; f1=finder(1,x1); f2=finder(1,x2); maxitr=50; tol=10^-6; if(f1*f2>0)
fprintf(“Invalid guess !!”); end err=zeros(1,maxitr);
for itr=1:1:maxitr m=(x1+x2)/2; fm=finder(1,m); err(itr)=abs(f2-f1); if(err(itr)<tol) break end if(f1*fm>0) x1=m;
f1=fm; else x2=m; f2=fm; end
end m figure(1) plot(err(1:itr-1),err(2:itr)) title(‘plot for bisection method’) end
m = 2.6180

Fixed Point Iterator;
function fpt() x=0.1; xold=x; maxitr=50; errfp=zeros(1,maxitr); tol=10^-6;
for itr=1:1:maxitr x=finder(2,xold); errfp(itr)=abs(x-xold); xold=x; if errfp(itr)<tol break end end x figure(2) plot(errfp(1:itr-1),errfp(2:itr)) title(‘plot for ftp method’) end
x = 0.3820

NEWTON METHOD
function newton() x=4;
maxitr=50; errnt=zeros(1,maxitr); tol=10^-6;
for itr=1:1:maxitr fx=finder(1,x); dfx=finder(3,x); xnew=x-fx/dfx; errnt(itr)=abs(xnew-x); if(errnt(itr)<tol) break end x=xnew;
end xnew figure(3) plot(errnt(1:itr-1),errnt(2:itr)) title(‘plot for newton method’) end function fval=finder(arg,xval) if arg==1 fval=xval^2-3*xval+1; elseif arg==2 fval=(xval^2+1)/3; else fval=2*xval-3; end end
xnew = 2.6180

Published with MATLAB® R2019b