how can i solve second order ODE with RK-4 without using a built in function in matlab?

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Mohammad Adeeb 2021-6-14

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https://ww2.mathworks.cn/matlabcentral/answers/855730-how-can-i-solve-second-order-ode-with-rk-4-without-using-a-built-in-function-in-matlab

评论： Mohammad Adeeb 2021-6-14

采纳的回答： Alan Stevens

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this is the equation :

(d^2 y)/(dt^2 ) + 3 (dy)/dt - 30t - 10 = 0

this is my code :

h=0.01;          %step size (changable according to the proplem)
t=0:h:1;        %the tdomain range
y = [1;-3]; %intial condition for first equation in form of matrix (changable according to the proplem)
for i = 1:length(t)-1
    
    K11 = RK4(t(i), y1(:, i));
    K12 = RK4(t(i) + h/2, y(:, i) + h*K11/2);
    K13 = RK4(t(i) + h/2, y(:, i) + h*K12/2);
    K14 = RK4(t(i) + h,   y(:, i) + h*K13);
    y(:, i+1) = y(:, i) + h/6*(K11 + 2*K12 + 2*K13 + K14);
    
end
function dy1 = RK4(t, y)
    f11 = y(2);
    f12 = -3*y(1)+30*t+10;
    dy1 = [f11;f12];
    %change the matrix due to your intital conditins 
                      %and the equation in your proplem
end