Usage of 'dsolve' function in MATLAB

I am trying to solve a 1D transient (unsteady state) partial differential equation of the form, du/dt = c (d2u/dy2). Here 'd' is actually partial differential because velocity (u) varies with time (t) and spacial coordinate (x) as well. c is a constant.

Initial condition

u(t=0) = 0

Boundary condition for the problem:

u(y=0,t) = - 0.001

u(y=80,t) = 0.001

Is it possible to use 'dsolve' function to get a solution to this transient problem ?

Also I need to plot the velocity (u) with distance (y) and check how the solution evolves over time.

Answer 1

[Torsten]

"dsolve" can be used for ordinary differential equations (1 independent variable).

Your equation is a partial differential equation (2 independent variables, namely t and y).

You will have to use a numerical solver to get a solution (e.g. "pdepe").

Best wishes

Torsten.