Can this differential equation be solved using matlab pdepe solver?

I'm looking to solve the PDE given below:

d2y/dx2 - y + f(x,t) = dy/dt

here - f(x,t) is a source term depending on location "x" and time "t"

Initial Condition: y(x,0) = 0

Boundary condition: y(x=0, t) = 0

y(x=L, t) = -dy/dx (robin boundary condition or mixed boundary condition at x = L; this is for convection)

Can this be solved using matlab's pdepe solver? If so, how? If not, what toolbox/command is needed to solve this type of PDE?

Answer 1

[Amit Bhowmick]

Look at this

https://in.mathworks.com/help/matlab/math/partial-differential-equations.html

[Akshay Deolia]

Hello Amit,

Thanks for your response. I'm particularly interested in solving the PDE with the "y" term in it, for example:

d2y/dx2 - "y" + f(x,t) = dy/dt. How can such an equation be solved in Matlab?

I can already solve the PDE without the "y" term in it i.e. the PDE: d2y/dx2 + f(x,t) = dy/dt

I solve it using the pdepe solver.

[Amit Bhowmick]

With y term you can solve, s would be s=-y+f(x,t), not sure about robin boundary conditions.