 # Numerical Analysis in Matlab

## Transcribed Text

1. For f(x) = sinz, approximate f'(Io) where To = 1.2 using the forward difference approximation /(sot))//(zo) Take h = 10", n = -20:0.5:0, use logging to plot h vs ab- solute of round off error and h vs discretization error( on the same graph. 2. Write a MATLAB code for Bisection Method to solve a nonlinear equation. Your function function[u] = bisect_method(func, a, b, fa, fb, tol) takes the inputs: a function, endpoints, values of function at these endpoints and tolerance. Use your code to solve 13 - 30x2 +2552 on [0. 20]. Display interval and function values at each iteration in columns.

## Solution Preview

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f=@(x)sin(x)

x0=1.2;

n=-20:0.5:0;

h=10.^n;

forward_diffs=(f(x0+h)-f(x0))./h;

figure;
loglog(h,abs(cos(x0)-forward_diffs),h,abs(.5*sin(x0)./h),'Linewidth',2);
xlabel('log h');
ylabel('log error');
legend('Absolute Error','Discretization Error','Location', 'best');
title('Forward Difference Derivative Errors');...
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