#### Numerical Modeling

###### Solution of non-linear boundry value problem using Finite Difference Approximation
• Used finite difference approximation method to discretize two-dimensional non-linear BVP and form couple of algebraic equations of the form R=0

• Solved the equations by implementing Newton' Method

• Tracked all the non-trivial solutions using analytical method and the arc length continuation method

• Used finite difference approximation method and discretized two-dimensional Poisson's equation and boundary conditions in the form of Ax = b

• Wrote MATLAB code to generate coefficient matrices 'A' and 'b' and solve for unknown 'x' using 4 different solvers:

• Intrinsic MATLAB solver

• LU Decomposition

• Jacobi solver, and

• Gauss-Seidel iterative solver

• Generated numerical solution for the problem with different grid sizes and compared scaling behavior and errors  for these methods

###### Solution of Lotka-Volterra system of equations using Euler methods
• Calculated critical points for the system of non-linear system of ordinary differential equations

• Set up solution equation based on both intrinsic and explicit Euler methods and performed accuracy analysis by varying the step size

• Analyzed phase plots and performed physical linear stability test

• Worked with 2 classmates and investigated coupled heat and hydrogen transfer processes in an annular cylindrical hydrogen storage device filled with five different metal alloys

• Adapted Finite Volume Method using central difference scheme and I wrote majority of around 1000 lines of code in C++ to simulate these transport equations

• Studied Hydrogen storage performance by varying the operating parameters, such as, hydrogen supply pressure, cold fluid temperature and overall heat transfer co-efficient

###### Analysis of Airbnb Reviews, hosts and user preferences

Airbnb, ever since its foundation in 2008, has impacted the travel experiences of people all around the world. In this project, I collected data from various internet sources, cleaned and modified for my analysis, and

• Predicted in which country a new Airbnb user will book his or her holiday based on information about their age, gender, nationality etc

• Studied hosts, and analyzed occupancy of different Airbnb listings in Austin, Texas

• Performed text mining to analyse user reviews

• Gathered data about hotels in Texas and visualized how presence of Airbnb has impacted the revenues of these hotels, to understand the impact of Airbnb on sharing economy.

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