Approximation Problem, replacing a power function

2013 11 6
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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.?

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