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4. The forward and backward finite-difference operators are defined by $D_+f(x) = \frac{f(x + h) - f(x)}{h}$, $D_-f(x) = \frac{f(x) - f(x - h)}{h}$. These operators can be applied sequentially, e.g., $D_+D_-f(x) = D_+(D_-f(x))$. 5 a) Implement the backward difference approximation $D_-f(x)$ and the central difference approximation $D_0f(x)$ to compute the derivative $f'(x)$ (defined in the class) in MATLAB. 5 b) Let $f(x) = \cos x$. Compute $D_0f$ and $D_-f$ at $x = \frac{\pi}{3}$ for $h = 0.1, 0.05, 0.025, 0.0125$. Report the errors for each $h$ by comparing against analytical solution. What is the order of accuracy for each method.

          4. The forward and backward finite-difference operators are defined by
$D_+f(x) = \frac{f(x + h) - f(x)}{h}$, $D_-f(x) = \frac{f(x) - f(x - h)}{h}$.
These operators can be applied sequentially, e.g., $D_+D_-f(x) = D_+(D_-f(x))$.
5 a) Implement the backward difference approximation $D_-f(x)$ and the central difference
approximation $D_0f(x)$ to compute the derivative $f'(x)$ (defined in the class) in MATLAB.
5 b) Let $f(x) = \cos x$. Compute $D_0f$ and $D_-f$ at $x = \frac{\pi}{3}$ for $h = 0.1, 0.05, 0.025, 0.0125$.
Report the errors for each $h$ by comparing against analytical solution. What is the order of
accuracy for each method.

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4. The forward and backward finite-difference operators are defined by
D+f(x) = (f(x + h) - f(x))/(h), D-f(x) = (f(x) - f(x - h))/(h).
These operators can be applied sequentially, e.g., D+D-f(x) = D+(D-f(x)).
5 a) Implement the backward difference approximation D-f(x) and the central difference
approximation D0f(x) to compute the derivative f'(x) (defined in the class) in MATLAB.
5 b) Let f(x) = cos x. Compute D0f and D-f at x = (π)/(3) for h = 0.1, 0.05, 0.025, 0.0125.
Report the errors for each h by comparing against analytical solution. What is the order of
accuracy for each method.

Added by Elizabeth S.

Computer Science and Information Technology

Trishna Knowledge Systems 2018 Edition

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Solved by Expert Florencia Cuzmar

Step 1

To implement the backward difference approximation D_f(x), we can use the formula: D_f(x) = (f(x) - f(x-h)) / h To implement the central difference approximation D0f(x), we can use the formula: D0f(x) = (f(x+h) - f(x-h)) / (2*h) Here is the MATLAB code to Show more…

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5 a) Implement the backward difference approximation D_f(x) and the central difference approximation D0f(x) to compute the derivative f'(x) (defined in the class) in MATLAB. 5 b) Let f(x) = cos x. Compute D0f and D_f at x = Ï€/3 for h = 0.1, 0.05, 0.025, 0.0125. Report the errors for each h by comparing against the analytical solution. What is the order of accuracy for each method? 4. The forward and backward finite-difference operators are defined by f(x+h)-f(x) and f(x)-f(x-h). These operators can be applied sequentially, e.g., D+D-f(x) = D+(D-f()). 5 a) Implement the backward difference approximation D-f(x) and the central difference approximation Dof(x) to compute the derivative f'(x) (defined in the class) in MATLAB. 5 b) Let f(x) = cos x. Compute Dof and D_f at x = T/3 for h = 0.1, 0.05, 0.025, 0.0125. Report the errors for each h by comparing against the analytical solution. What is the order of accuracy for each method?

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