Nonlinear PDE finite difference method

[Hassen]

Hello
I want to resolve a nonlinear partial differential equation of second order with finite difference method in matlab. the equation is in the pdf file attached.
Thanks

 

[bigfooted]

Cool! Have fun!

 

[Hassen]

please can you help me in doing this..

 

[bigfooted]

Can you give some additional information?
Where does this equation come from? Did you derive it yourself? Is it possible that some terms can be neglected because they are small? What are the dimensions (units) of all the variables? Can you check that each of the terms has the same dimensions/units? Why do you need to solve it?

Also, you have $\frac{dC}{dt}$ as well as $\frac{2}{dt}$, which seems a bit odd. Or do you mean that you take the time derivative of this big square-root term? You also mix derivatives with partial derivatives.

If you give the context of this equation, some people here will probably be able to tell you immediately what a common way to proceed would be.

 

[Hassen]

Thank you
sorry I made some mistakes in the equation the new version is in the joint file.
dt mean a time step and not a derivatives.
and all the other terms are partial derivaties.
this equation is PDE of option pricing in presence of transaction costs and stochastic volatility from this article http://www.math.stevens.edu/~ifloresc/Research/Publications/OptionPriceswithTransactionCostsSV.pdf
page 11 equation (2.12) (I just add a term to this equation)
I want to simulate the call price C.

 

[Hassen]

??