Notes

Bisection Method Code:

clear all clc f=input(' Enter a function: '); a=input(' Enter start of interval: '); b=input(' Enter end of interval: '); e=input(' Enter percentage error: '); if (feval(f,a)==0) display('a is the root of the equation ' ); elseif (feval(f,b)==0) display('b is the root of the equation ' ); elseif feval(f,a)*feval(f,b)> 0 display (' this interval is invalid '); else xn=(a+b)/2; while (abs((xn-a)/(xn))*100>e || abs((xn-b)/(xn))*100>e) if feval(f,a)*feval(f,b)<0 xn=(a+b)/2; f_xn=feval(f,xn); if f_xn*feval(f,a)<0 b=xn; elseif f_xn*feval(f,a)>0 a=xn; else display(xn + 'is the root') end end end display (' the root is ') ; disp(xn) end

Newton Raphson Method Code:

clear all clc f=input(' Enter a function: '); x0=input(' Enter the intial guess: '); e=input(' Enter percentage error '); fdiff= input(' please enter derivative of the function '); if (feval(f,x0)==0) display('x0 is the root of the equation ' ); else xn=x0-(feval(f,x0)/feval(fdiff,x0)); en=abs((xn-x0)/xn)*100; while en>e xn=x0-feval(f,x0)/feval(fdiff,x0); en=abs((xn-x0)/xn)*100; x0=xn; end disp('the root is: ') disp(xn) end

Lagrange Interpolation Code:

clear all clc X=input('Enter the values of x in vector form: '); Y=input('Enter the values of f(x) in vector form: '); p=input('Enter the point to interpolate at: '); n=length(X); degree=n-1; syms x m=1; for i=1:n for j=1:n if i~=j l(m)=(x-X(j))./(X(i)-X(j)); m=m+1; end end L(i)=prod(l); m=1; end poly=sum(Y(1:n).*L); s=simplify(poly); display('The value of the polynomial at x= ') disp(subs(s,p))