Work

A fourth-order RBF-FD scheme based on integral representations of the multiquadric for high-dimensional Black–Scholes PDEs

Year: 2026

Type: article

Abstract: The valuation of multi-asset European options poses major challenges due to the curse of dimensionality. We present a fourth-order meshless radial basis function-produced finite difference (RBF-FD) approach based on a modified multiquadric kernel and its integral representations. This construction yields analytical differentiation weights on specific five-point stencils and enables efficient spatial discretization. Numerical experiments confirm the method’s stability, efficiency and convergence.

Source: Engineering Analysis with Boundary Elements

DOI: 10.1016/j.enganabound.2026.106673

Author: Yanlai Song

Institution: Zhongyuan University of Technology

Language: English

Topic: Numerical methods in engineering

Subfield: Mechanics of Materials

Field: Engineering

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,590

Funder: Zhongyuan University of Technology