During the past decade, various accurate modeling methods have been developed for modal analysis of different photonic devices. These methods included the finite‐difference method (FDM), the finite ...

This chapter discusses in detail the basic principles and formulations of the full‐vectorial finite‐difference time domain (FDTD) method. It presents the basic idea of the FDTD method to solve Maxwell ...

A new approach in the finite difference framework is developed, which consists of three steps: choosing the dimension of the local approximation subspace, constructing a vector basis for this subspace ...

We develop here a finite-difference approach for valuing a discretely sampled variance swap within an extended Black–Scholes framework. This approach incorporates the observed volatility skew and is ...

The finite difference method is a numerical technique that approximates derivatives with finite differences. This methodology can be used to solve the heat equation. A strong overview of this ...

A new high-order hybrid method integrating neural networks and corrected finite differences is developed for solving elliptic equations with irregular interfaces and discontinuous solutions. Standard ...