Question about initial value problem

I really do not understand what this question says to me. In those quarantina days, I am trying to learn matlab by myself by using Tobin's book. thus, I have no body to ask directly this question. Therefore, I posted this question without any my solution trial. sorry for that. any help, any suggestion any hint to give a way to solve this question will become very useful for me. Many thanks.

Answer 1

[Ameer Hamza]

This question is similar to the one you posted earlier from this book, but this time, instead of giving a function handle as input, we are only giving vectors x and y. The interquad function does not know the input function and just need to rely on these data points to find the integral. To guess the value at a point, not in vector x, we use interpolation. Try the following code to

x = 0:0.01:1;
y = x.^2;

a = interquad(x, y);

function Q = interquad(x, y)
    f = @(xq) interp1(x, y, xq, 'pchip'); % phicp is recommended instead of cubic
    Q = quad(f, x(1), x(end));
end

It creates vectors x, and y from function on the interval . The output is as follow

a =
    0.3333

It is same as integral of on interval 0 to 1.

[Zeynep Toprak]

Dear Hamza, your solutions are very useful. I saw similar auestion, but I am stack at it due to different function types. I dont knoe how to deal with this function type. but as a result of your great solution, I see it! really really thank you so much. And also, if you have time, please can you look at my any other question on boundary value problem. I want to see one example of boundary value problem in matlab. this is a good example in the book. can you help me to do this? My question so Link Many many thanks!

[Ameer Hamza]

I am glad to be of help. Check my answer on that question.