George Mason University

Zakaria Tarik Zerhouni

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Math 447: Numerical Analysis

Project 1

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2. Plot the solution from Step 1 against the correct solution: $$y(x)=\frac{f}{24EI}x^2(x^2-4Lx+6L^2)$$ where $f=f(x)$ is constant defined above. Check the error at the end of the beam, $x=L$ meters. In this simple case the derivative approximations are exact, so your error should be near machine round off.

The error at $x = L$ was computed as $-6.591949208711867e-16$.
Machine epsilon, denoted as $\epsilon_{mach} = 2^{-52}$ is the distance between 1 and the smallest floating point number greater than one. In this way it defines the bounds of computing accuracy for IEEE double precision floating point standard. As $\epsilon_{mach} \approx 2.22e-16$, the result returned for the error at $x = L$ is near machine round-off.

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