How to solve a set of non linear equations using second order newton raphson method in matlab?

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Varun Agrawal 2015-5-15

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https://ww2.mathworks.cn/matlabcentral/answers/216843-how-to-solve-a-set-of-non-linear-equations-using-second-order-newton-raphson-method-in-matlab

评论： Varun Agrawal 2015-5-28

I want to solve the following set of equations to find unknown alpha values(V and r values are known). Can anybody help me with this?

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Varun Agrawal 2015-5-28

I have written a code by taking an example for which the final answer is known. But it is not giving the numerical values and gives expressions instead. Can anybody help me out?

v_mean = 3.089; v_sq_mean = 18.344; v_cu_mean = 191.042; v_min = 0; v_max = 17;

syms x a b c d

F1 = int(exp(-a-(b.*x)-(c.*x.^2)-(d.*x.^3)),v_min,v_max) - 1;

F2 = int(x.*(exp(-a-(b.*x)-(c.*x.^2)-(d.*x.^3))),v_min,v_max) - v_mean;

F3 = int((x.^2).*exp(-a-(b.*x)-(c.*x.^2)-(d.*x.^3)),v_min,v_max) - v_sq_mean;

F4 = int((x.^3).*exp(-a-(b.*x)-(c.*x.^2)-(d.*x.^3)),v_min,v_max) - v_cu_mean;

J11 = diff(F1,a);

J12 = diff(F1,b);

J13 = diff(F1,c);

J14 = diff(F1,d);

J21 = diff(F2,a);

J22 = diff(F2,b);

J23 = diff(F2,c);

J24 = diff(F2,d);

J31 = diff(F3,a);

J32 = diff(F3,b);

J33 = diff(F3,c);

J34 = diff(F3,d);

J41 = diff(F4,a);

J42 = diff(F4,b);

J43 = diff(F4,c);

J44 = diff(F4,d);

abcd = zeros(4,1);

error=1; while error > 0.0001

a=abcd(1,1); b=abcd(2,1); c=abcd(3,1); d=abcd(4,1);

J = [vpa(J11) vpa(J12) vpa(J13) vpa(J14) vpa(J21) vpa(J22) vpa(J23) vpa(J24) vpa(J31) vpa(J32) vpa(J33) vpa(J34) vpa(J41) vpa(J42) vpa(J43) vpa(J44)];

J_inverse = inv(J);

F = [vpa(F1) vpa(F2) vpa(F3) vpa(F4)];

JF = (J_inverse)*F;

abcd = abcd - JF;

error = sum(JF)

end

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