roots findings 1
TRANSCRIPT
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ROOTS FINDINGSMuhammad Arslan
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Overview
• Introduction
• Plotting
• Fixed Point Iteration
• Bisection Method
• Newton Raphson Method
• Secant Method
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Introduction
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Plotting
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Fixed Point Iteration
clear allxinit=input(‘Enter the initial value of x’);
f=@(x)2*sin(x.^2);
xnext=f(xinit);
while(abs(xnext-xinit)>1e-4)
xinit=xnext;
xnext=f(xinit);end
disp([‘ Root is ‘ num2str(xnext)]);
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Bisection
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Newton Raphson Method
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clear all
x(1)= input(‘ Starting guess ’);
f=@(x)exp(x)-exp(-2*x)+1;
fp=@(x)exp(x)+2*exp(-2*x);
for i=1:100x(i+1)=x(i)-f(x(i))/fp(x(i));
if(x(i+1)==x(i))
break;
end
end
x(end)
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Or Alternatively
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Secant Method
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Clear all
x(1)= input(‘ Starting guess 1 ’);
x(2)= input(‘ Starting guess 2 ’);
f=@(x)3*x+sin(x)-exp(x);
for i=1:100x(i+2)=x(i)-f(x(i))*(x(i+1)-x(i))/(f(x(i+1))-f(x(i)));
if(x(i+2)==x(i+1))
break;
end
end
x(end)