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# How to solve a set of coupled ODEs (4th Order)?

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Shashank on 28 Jun 2013
Could somebody help me solve this set of four coupled ODEs?
tpcl = @(xi,y) [y(2); ((1 + (y(2)*y(2)))^(1.5))*(y(3) - (A/(y(1)^3)))/sigma; -3*mu_l*y(4)/(rho_l*h_lv*(y(1)^3)); (Twall - Tsat - (Tsat*y(3)/(rho_l*h_lv)))/((y(1)/k_l) + R_int)];
xi_step = 0:1e-8:xi_end;
[XI,Y] = ode15s(tpcl,xi_step,[delta_ad deltaprime_ad delta_p_ad Q_ad]);
I tried both ode45 and ode15s, but the results are unrealistic/ The constants used here are as follows:
A = 1e-20;
R_FC = 24.597;
c = 1;
sigma = 0.01;
rho_l = 1593.84;
k_l = 0.0544;
mu_l = 0.0004683;
rho_v = 11.61;
h_lv = 88000;
Twall = 334;
Tsat = 329;
R_int = ((2 - c)/(2*c))*(Tsat^(1.5))*((2*pi*R_FC)^(0.5))/(rho_v*(h_lv^2));
delta_ad = (A/(rho_l*h_lv*((Twall/Tsat) - 1)))^(1/3);
deltaprime_ad = 0;
delta_p_ad = A/(delta_ad^3);
Q_ad = 0;
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