As a master student, I worked on partial differential equations, integral equations and approximation theory specially wavelets. For solving these types of equations I implemented Projection methods such as collocation, galerkin and petov-galerkin methods. For analysis of convergency of these methods, I worked on linear and nonlinear functional analysis specially compact and complete continuous operators and index theory. In approximation theory field, I was working on local basis functions such as cardinal splines and wavelets specially biorthogonal spline and multi-wavelets.
Partial Differential Equations
Numerical Solution of Stochastic Differential Equation
"Numerical Algorithm for Pricing of Discrete Barrier Option in a Black-Scholes Model", R.Farnoosh, Hamidreza Rezazadeh, Amirhossein Sobhani , Masoud Hassanpour International Journal of Nonlinear Analysis and Applications. (Accepted).
"A Semiparametric Estimation for Regression Functions in the Partially Linear Vector Autoregressive Time Series Model", R.farnoosh, M Hajebi, Amirhossein Sobhani.