IMEX-RK finite volume methods for nonlinear 1d parabolic PDEs Application to option pricing
<|reference_start|>IMEX-RK finite volume methods for nonlinear 1d parabolic PDEs Application to option pricing: The goal of this paper is to develop 2nd order Implicit-Explicit Runge-Kutta (IMEX-RK) finite volume (FV) schemes for solving 1d parabolic PDEs for option pricing, with possible nonlinearities in the source and advection terms. The spatial semi-discretization of the advection is carried out by combining finite volume methods with 2nd order state reconstructions; while the diffusive terms are discretized using second-order finite differences. The time integration is performed by means of IMEX-RK time integrators: the advection is treated explicitly, and the diffusion, implicitly. The obtained numerical schemes have several advantages: they are computationally very efficient, thanks to the implicit discretization of the diffusion in the IMEX-RK time integrators, which allows to overcome the strict time step restriction; they yield second-order accuracy for even nonlinear problems and with non-regular initial conditions; and they can be extended to higher order.<|reference_end|>
@article{lópez-salas2024imex-rk,
    title={IMEX-RK finite volume methods for nonlinear 1d parabolic PDEs.
  Application to option pricing},
    author={J. G. L'opez-Salas, M. Su'arez-Taboada, M. J. Castro, A. M.
  Ferreiro-Ferreiro and J. A. Garc'ia-Rodr'iguez},
    journal={L\'opez-Salas, J.G. et. al. IMEX-RK Finite Volume Methods for
  Nonlinear 1d Parabolic PDEs. Application to Option Pricing. In: Hyperbolic
  Problems: Theory, Numerics, Applications. SEMA SIMAI Springer Series, vol 35.
  Springer, Cham, 2024},
    year={2024},
    doi={10.1007/978-3-031-55264-9_36},
    archivePrefix={arXiv},
    eprint={2409.01125},
    primaryClass={math.NA cs.NA math.AP}
}