A fourth-order RBF-FD scheme based on integral representations of the multiquadric for high-dimensional Black–Scholes PDEs
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.
Fields of Study & Subjects
Numerical methods in engineering
Advanced Numerical Methods in Computational Mathematics
Model Reduction and Neural Networks
Publication details
- Journal / source
- Engineering Analysis with Boundary Elements
- Publisher
- Elsevier BV
- Volume
- 185
- Pages
- 106673–106673
- Publication date
- 4 February 2026
- Language
- EN