This paper presents an approach for solving a nonlinear stochastic differential equations (NSDEs) using a new basis functions (NBFs). These functions and their operational matrices are used for representing matrix form of the NBFs. With using this method in combination with the collocation method, the NSDEs are reduced a stochastic nonlinear system of equations and unknowns. Then, the error ana...

This paper introduces a numerical method for solving the vasicek model by using a stochastic operational matrix based on the triangular functions (TFs) in combination with the collocation method. The method is stated by using conversion the vasicek model to a stochastic nonlinear system of $2m+2$ equations and $2m+2$ unknowns. Finally, the error analysis and some numerical examples are provided...

The CUR matrix decomposition and the Nyström approximation are two important lowrank matrix approximation techniques. The Nyström method approximates a symmetric positive semidefinite matrix in terms of a small number of its columns, while CUR approximates an arbitrary data matrix by a small number of its columns and rows. Thus, CUR decomposition can be regarded as an extension of the Nyström a...

Smart meters (SMs) are being widely deployed by distribution utilities across the U.S. Despite their benefits in real-time monitoring. SMs suffer from certain data quality issues; specifically, unlike phasor measurement units (PMUs) that use GPS for synchronization, not perfectly synchronized. The asynchrony error can degrade monitoring accuracy networks. To address this challenge, we propose a...