RBF-FD formulas have received special attention due to their superior accuracy, well-
conditioning, and ease of implementation in solving partial differential equations. To further …

In this work, a new linearized alternating direction implicit (ADI) compact difference method
(CDM) is proposed for solving nonlinear two-dimensional (2D) and three-dimensional (3D) …

Proper pricing of options in the financial derivative market is crucial. For many options, it is
often impossible to obtain analytical solutions to the Black–Scholes (BS) equation. Hence an …

There exist several numerical methods for finding the resolution of high dimensional option
pricing Black-Scholes PDE with variable coefficients. Here we use radial basis functions to …

To overcome a significant challenge in traditional parameterized level set methods based on
globally supported radial basis functions, we propose employing a local differentiation …

Recently, several improvements over the radial basis function generated finite difference
method have been appeared numerically and theoretically in literature. Suitable …

The purpose of this article is to study how the integrals of the Gaussian radial basis function
can be employed to produce the coefficients of approximations under the radial basis …

We propose an overlapping algorithm utilizing the K-means clustering technique to group
scattered data nodes for discretizing elliptic partial differential equations. Unlike …

In this paper, we investigate the numerical valuation of European and American options
under the time fractional Black-Scholes model. We first apply a coordinate stretching …

We consider the problem of approximating a linear differential operator on several specific
stencils using the radial basis function method in the finite difference scheme. We prove a …