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Numerically solving first-order integro-differential equation

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AHMAD TALAEI
AHMAD TALAEI 2020-11-13
编辑： AHMAD TALAEI 2020-11-13
Can anyone help me solve the following equation numerically:
where a = 8, b = 5.3e+04, c = 22, d = 2, e = 100, and v(0) = eps.
I wrote the following code for t in the range 0 to 1, but there is an error with the integral term.
clear all
clc
syms v_p(t) t
eqn(1) = diff(v_p,1) == -8 - CD(v_p)*abs(v_p)*v_p - 5.3e4*Int(v_p,t);
pretty(eqn)
[V] = odeToVectorField(eqn);
fun = matlabFunction(V,'Vars', {'t','Y'});
tInterval = [0 1];
vInit = [eps];
vSol = ode45(fun,tInterval,vInit);
tValues = linspace(tInterval(1),tInterval(2),100);
vValues(1:length(tValues)) = deval(vSol,tValues,1);
plot(tValues,-vValues)
function getCD = CD(v_p)
getCD = 22 + 2/abs(v_p) + 100/(1+sqrt(abs(v_p)));
end
function getInt = Int(v_p,t)
T = linspace(0,t);
Int_diff = zeros(1, length(T));
for i = 1:length(T)
[~, y] = ode45(@(s,y) diff(v_p,s)/sqrt(T(i)-s), [0 T(i)+eps], eps);
Int_diff(i) = y(end);
end
getInt = Int_diff(end)
end

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