Abstract: <p>The time-dependent Gross-Pitaevskii Equation, describing the movement of parti-</p><p>cles in quantum mechanics, may not be solved analytically due to its inherent non-</p><p>linearity. Hence numerical methods are of importance to approximate the solution.</p><p>This study develops a discrete scheme in time and space to simulate the solution</p>… more
Abstract: <p>In this thesis, a new sinc-collocation method based upon derivative interpolation is developed for solving linear and nonlinear boundary value problems involving differential as well as integro-differential equations. The sinc-collocation method is chosen for its ease of implementation, exponential convergence of error, and ability to handle to singularities in the BVP. We present a… more
