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

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Abstract

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.

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Acknowledgements

The authors are thankful to an anonymous referee whose comments and suggestions helped improve this paper.

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Authors and Affiliations

  1. Department of Mathematics, Institute for Advanced Studies in Basic Sciences (IASBS), Zanjan, 45137-66731, Iran

    Fazlollah Soleymani

  2. Department of Mathematics, King Abdulaziz University, Jeddah, 21589, Saudi Arabia

    Malik Zaka Ullah

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  1. Fazlollah Soleymani
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  2. Malik Zaka Ullah
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Correspondence to Fazlollah Soleymani.

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Soleymani, F., Zaka Ullah, M. A multiquadric RBF–FD scheme for simulating the financial HHW equation utilizing exponential integrator. Calcolo 55, 51 (2018). https://doi.org/10.1007/s10092-018-0294-z

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