Differential and Integral System

Can a system of differential and integral equations be solved in Matlab? I have the following system): y1'+a*(y1-y3)=0; y2'+b*(y2-y4)=0; intg(y1-y3) + c*y3- d*(y3*y4)=0; intg(y2-y4) + c*y4- e*(y3*y4)=0;

Answer 1

[Torsten]

Set

y5=intg(y1-y3)
y6=intg(y2-y4)

Then your system becomes

(1) y1'+a*(y1-y3)=0
(2) y2'+b*(y2-y4)=0
(3) y5 + c*y3- d*(y3*y4)=0
(4) y6 + c*y4- e*(y3*y4)=0
(5) y5'=y1-y3
(6) y6'=y2-y4

Use equations (3) and (4) to solve for y3 and y4.

Best wishes

Torsten.

[AMEYA T]

Thanks for the answer. This scheme is good but, I will have to estimate the initial values of the new variables y5 and y6 for passing them as an argument to ODE solver, which I think is not possible unless one solves the system.

[Torsten]

The initial values of y5 and y6 are both equal to 0.

Best wishes

Torsten.