MATLAB: Solve a coupled pair of non-linear differential delay equations

coupled differential equationsdelay equationsnonlinear differentials

Hello, Is it possible in Matlab to solve a coupled pair of non-linear differential delay equations? In particular the equations I am interested is: p'[t] = -(p[t – 2] – q[t – 2])^3/2 , q'[t] = (p[t – 2] – q[t – 2])^3/2, p[t /; t < 0] == 1.01 + 0.1*(t – 3), p, q[t /; t < 0] == 1.0 – 0.1*(t – 3), q, {t, -2, 10}

Best Answer

Adding your equations gives

p'(t)+q'(t)=0,

p(t)=-q(t)+constant

Inserting in the second equation gives

q'(t)=(-2*q(t-2)+constant)^3/2

"constant" can be determined from your history initial conditions for p and q.

Best wishes

Torsten.

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MATLAB: How to get the coefficient of this symbolic expression

Try this. C vector contains the coefficient

ti=0; tf=2;
h=0.5;
tt=ti:h:tf+h;
i=2;
syms q(t) p(t) d(t) g(t) y(t)
q(t)=1;
p(t)=t;
d(t)=0;
g(t)=2-abs(1-t);
aa=q(t)*(y(i+1)-2*y(i)+y(i-1))/h^2+p(tt(i))*(y(i+1)-y(i-1))/(2*h);
syms x
C = zeros(1,3);
for i=1:3
    temp = coeffs(subs(aa,y(i),x));
    C(i) = temp(2);
end

MATLAB: I am solving a system of non linear equation using vpasolve but it shows answer as [0*1sym] any other method that I can use

a1 = (-44*Pi^4-1875*P1)*R/(9600*Pi^4*R-1100*Pi^4-75*P3)
a2 = (-1188*Pi^4-625*P2)*R/(19200*Pi^4*R-3300*Pi^4-225*P3)
a3 = R

where

R = roots([2899102924800000000000*Pi^20, -113246208000000000000*Pi^16*((44/3)*Pi^4+P3), 4423680000000000000*((108416/146484375)*Pi^10+(243960584/3515625)*Pi^8+((88/1875)*P1+(594/625)*P2+(814/75)*P3)*Pi^4+P1^2+(1/4)*P2^2+(37/100)*P3^2)*Pi^12, -103680000000000000*((44/3)*Pi^4+P3)*((16153984/10986328125)*Pi^10+(35264208/9765625)*Pi^8+((88/1875)*P1+(396/625)*P2+(44/15)*P3)*Pi^4+P1^2+(1/6)*P2^2+(1/10)*P3^2)*Pi^8, 607500000000000*((44/3)*Pi^4+P3)^2*Pi^4*((30464896/6591796875)*Pi^10-(1931850032/52734375)*Pi^8+((88/1875)*P1+(264/625)*P2+(88/75)*P3)*Pi^4+P1^2+(1/9)*P2^2+(1/25)*P3^2), -86016*(11011*Pi^2-75623375)*Pi^8*(44*Pi^4+3*P3)^3, 11760*Pi^4*(44*Pi^4+3*P3)^4*(121*Pi^2-432125), -(847*Pi^2+125)*(44*Pi^4+3*P3)^5])

... All of the roots. The polynomial is degree 7, so there will be 7 roots, and so 7 solutions to the overall equations.

Best Answer

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MATLAB: How to get the coefficient of this symbolic expression

MATLAB: I am solving a system of non linear equation using vpasolve but it shows answer as [0*1sym] any other method that I can use

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