I want to ask for help and guidance to know if the following problem can be solved using ApproxFun, as I have not encountered any example doing a similar thing.
Consider, for instance, a linear system of differential algebraic equations with the following form
u' + av = \lambda v, \\
v' + w + au = \lambda (u + bz), \\
aw + cu = \lambda w, \\
az = \lambda (z + bu),
subjected to the boundary conditions u(0.5)=u(1)=0. Since this system does not have a derivative and a boundary condition for each equation, I am not sure it fits the template of problems that ApproxFun can handle, but I am very interested to know if this library can be used to analyze such problems.