Euler’s method

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Edinson Manga 2020-5-26

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https://ww2.mathworks.cn/matlabcentral/answers/533573-euler-s-method

编辑： darova 2020-5-27

How make the map of integral curves in the region [0, 10] × [0, 10] of the differential equation y′(t) = (y (t) - 5) (cos2 (t) - 0.5) graphing simultaneously, for k = 0, 1,. . . , 10, the solution obtained using Euler's method with step h = 0.01 and with initial condition y (0) = k.

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Edinson Manga 2020-5-26

Hi Darova, this is my first attempt, but I am having trouble correctly writing the function, what do you think?

Edinson Manga 2020-5-26

H = [0.01]; 
Y_euler = cell(1,numel(H));
for j=1:numel(H)
    h = H(j);
    x = 0:h:10;  
    y = zeros(1, numel(x)); 
    y(1) = 1;  
    n = numel(y); 
    for i=1:n-1
        f = ((y(x)-5)*(cos(x)^2)-0.5));
        y(i+1) = y(i) + h * f;
    end
    Y_euler{j} = [x; y].';
end
syms Y(X)
eq = diff(Y) == (Y-5)*(cos.^2)-0.5));
for i=0:10
ic = Y(0) == i;
i=i+1;
sol = dsolve(eq, ic);
y_sol = double(subs(sol, X, x));
hold on
plot(x, y_sol, 'r', 'DisplayName', 'true solution');
for k=1:numel(H)
    plot(Y_euler{j}(:,1), Y_euler{j}(:,2), 'b--', 'DisplayName', ['Euler method h=' num2str(H(k), '%.3f')]);
end
end