Approximation Problem, replacing a power function

Dears

I am working on an ode and I am using the ode15s solver. The ode contains a nonlinear term , when using the finite volume discretization which is

((Y(i+1)-y(i))/dx)^a

The solver is not working and it was busy for 4 days.....

I am thinking to approximate this value( linearization)

Any one has an idea how to linearize this term.?