Can someone help me generate numerical values ​​for this sample problem using bvp4c solver?

y'' + y = 0

Boundary conditions are y(0)=1; y(pi/2)=0.

Compute y(pi/3) and y(pi/4) using MATLAB Bvp4c solver.

Can someone help me generate numerical values for this sample problem using bvp4c solver?

I want code command to generate the values of y(pi/3) and y(pi/4).

Trial code

function sampletrial
clear all;
close all;
clc;
gva=[pi/3 pi/4];
for i=1:2
    g=gva(i);
    figure(1);
    solinit=bvpinit(linspace(0,pi/2,50),[1 0]);
    sol=bvp4c(@shootode5,@shootbc5,solinit);
    eta=sol.x;
    f=sol.y;
    plot(eta,(f(1,:)),'--','linewidth',2);
    hold on
end

    function dydx=shootode5(eta,f)
        dydx=[f(2)
            -f(1)];
    end

    function res=shootbc5(fa,fb)
        res=[fa(1)-1
            fb(1)];
    end

Answer 1

[Rajeev]

Can you try adding the line:

y_values(i) = interp1(sol.x, sol.y(1,:), g);

in the loop?

[VAIDEHI]

Thank you sir.

This command worked for me. I got the values of cos(pi/3) and cos(pi/4) without putting a semicolon at the end.

y_values(i) = interp1(sol.x, sol.y(1,:), g)

Verified.