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Im trying to solve the following diffusion problem using crank Nicholson method, but having trouble on how to proceed with the tridiagonal matrix and boundary conditions.

dy/dt = k* d^2y/dx^2 K = increases with x

My initial condition is y(x,0)=0;

Boundary conditions are

dy/dx (at y=0) = z (z changes with time step)

d^2y/dx^2 (at y=1) = 0 (y goes from 0 to 1,n=10)

I need to solve for y(0 to 1) for 1 timestep at a time. Y becomes nonzero everywhere after a particular time.

any inputs in how to solve is greatly appreciated.

thanks

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# Diffusion problem

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