applying newton's method

I have some problems since I didn't know how to put the function of the parabola and then applying newton's method in that specific example.

Assume that the left ventricular pressure (LVP) can be represented as a parabola with peak systolic pressure of 120 mmHg and the mean aortic pressure of 90 mmHg. Assume that the peak is reached at half of a cycle with duration a unit time.

(a) Find the time at which the aortic valve opens and the time at which it closes, using the Newton method.

(b) Find these times if the peak pressure ranges from 120 mmHg to 100 mmHg and from 120 mmHg to 140 mmHg. Make a plot.

Hint: Opening and closing of the aortic valve occur approximately at the point when the mean pressure intercepts the LVP curve.

Hint: The formula for an inverted parabola with vertex at (h, k) and focus at (h, k + p) is (x − h) 2 = −4p(y − k).

Answer 1

[Sam Chak]

Hi @Romaisa Abdeselam Lazrak

You can find the examples related to Newton-Raphson method in this link:

https://www.mathworks.com/matlabcentral/answers/1685284-help-with-newton-raphson

Post your MATLAB code later once you learned how to apply it in your problem.