A multiquadric RBF–FD scheme for simulating the financial HHW equation utilizing exponential integrator

We propose a computational scheme to solve the financial time-dependent 3D Heston–Hull–White PDE. In fact, a novel radial basis function (RBF) generated finite difference (FD) scheme associated with multiquadric RBF is introduced for solving this convection–diffusion–reaction equation. Non-uniform g...

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Bibliographic Details
Published in:Calcolo 2018-12, Vol.55 (4), p.1-26, Article 51
Main Authors: Soleymani, Fazlollah, Zaka Ullah, Malik
Format: Article
Language:English
Subjects:
Basis functions
Computer simulation
Convection
Finite difference method
Mathematics
Mathematics and Statistics
Numerical Analysis
Radial basis function
Reaction-diffusion equations
Theory of Computation
Time dependence
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Summary:We propose a computational scheme to solve the financial time-dependent 3D Heston–Hull–White PDE. In fact, a novel radial basis function (RBF) generated finite difference (FD) scheme associated with multiquadric RBF is introduced for solving this convection–diffusion–reaction equation. Non-uniform grids alongside the multiquadric RBF–FD technique are applied to obtain results of high accuracy in significant areas, at which the PDE problem is degenerate and discontinuous. The efficacy of the new scheme is shown through a series of numerical experiments.
ISSN:0008-0624
1126-5434
DOI:10.1007/s10092-018-0294-z