Nonlinear PDE finite difference method

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Discussion Overview

The discussion centers around resolving a nonlinear partial differential equation (PDE) of second order using the finite difference method in MATLAB. The context involves option pricing in the presence of transaction costs and stochastic volatility, as referenced in a linked article.

Discussion Character

  • Technical explanation
  • Homework-related

Main Points Raised

  • One participant seeks assistance in implementing a finite difference method for a nonlinear PDE.
  • Another participant requests additional information about the origin of the equation, its derivation, and the dimensions of the variables involved.
  • Concerns are raised about the notation used, specifically regarding the time derivative and the mixing of derivatives with partial derivatives.
  • The original poster clarifies that the equation is related to option pricing and provides a reference to a specific article, noting an adjustment made to the equation.

Areas of Agreement / Disagreement

The discussion remains unresolved, with multiple questions and clarifications sought regarding the equation and its context. No consensus has been reached on the approach to solving the PDE.

Contextual Notes

Participants have noted potential issues with the equation's notation and the need for clarification on the dimensions of the variables. The discussion highlights the importance of context in understanding the equation's application.

Hassen
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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
 

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Cool! Have fun!
 
please can you help me in doing this..
 
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.
 
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.
 

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