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
"A Numerical Method for Pricing Discrete Double Barrier Option by Legendre Multiwavelet", Amirhossein Sobhani, Mariyan Milev.
"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.