I have a delayed partial differential equation to be solved because MMA cannot solve directly. I just used the method of this post Solve PDE with complicated coefficient non-linearity to transform it into a system of delayed ordinary differential equations. However, when trying to solve the system of delay ordinary differential equations, I encountered an error reported by the program. It says that integral variables are not real numbers. This is the equation I tried. $$v\left( t \right) -w\left( t \right) -v''\left( t \right) =0$$ $$v (t) + 2 w (t) + w'' (t)-\exp (-\eta t)\int_ 0^t\exp (x) w (x)\, \mathrm dx = \exp (t)$$ The equations is a ordinary differential equations with delay integral, which I got arbitrarily. The key point of the equations have an integral function. Their initial condition is 0. Here is the code I tried.
ode = {v[t] - w[t] - Derivative[2][v][t] == 0, v[t] + 2*w[t] + Derivative[2][w][t] - Exp[-\[Eta]t]*Integrate[Exp[x]*w[x], {x, 0, t}] == Exp[t]};
ics = {v[0] == 0, Derivative[1][v][0] == 0, w[0] == 0, Derivative[1][w][0] == 0};
rs = Apply[Set, Flatten[NDSolve[{ode, ics}, {v, w}, {t, 0, 5}]], {1}]
Here is the result I got, which says $x$ isn't a real number. HELP!
Set@@@
in your code? What are you trying to achieve with this? Also, it's not hard to notice the solution to the system isw[t]==v[t]==0
, if it should not, something is probably wrong with the system, please double check it. $\endgroup$Set@@@
before you've successfully resolved the equation. $\endgroup$