1. Question raised:
This equation comes from the mathworks forum l
This kind of equation is called integral-differential equations, which is roughly a differential equation with an integral term. The integral must be a definite integral. Some of these equations are integrals with variable upper and lower limits, and the upper and lower limits are x or other differential functions.
As usual, analyze first. The integral interval is 0-1, x is the independent variable, and y is the dependent variable. Except for the integral, other conditions are known. The values required for dy of different orders are as follows:
The more troublesome thing is the integral. The integral needs to know the values of all time points of y'(t) in advance, but when ode45 is solved, it is gradually integrated from 0-1 according to the time. The initial value has not yet been determined. The entire integral data It didn't come out yet, how can you score points? This is obviously a contradiction.
Two, the solution
After research, there are many solutions to this equation, and a simple method is mentioned here. The reference paper is