Second order finite volume IMEX Runge-Kutta schemes for two dimensional parabolic PDEs in finance
<|reference_start|>Second order finite volume IMEX Runge-Kutta schemes for two dimensional parabolic PDEs in finance: We present a novel and general methodology for building second-order finite volume implicit-explicit Runge-Kutta numerical schemes for solving two-dimensional financial parabolic PDEs with mixed derivatives. The methods achieve second-order convergence even in the presence of non-regular initial conditions. The IMEX time integrator allows to overcome the tiny time-step induced by the diffusive term in the explicit schemes, also providing accurate and non-oscillatory approximations of the Greeks.<|reference_end|>
@article{lópez-salas2024second,
    title={Second order finite volume IMEX Runge-Kutta schemes for two dimensional
  parabolic PDEs in finance},
    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={J.G. L\'opez-Salas et. al. Second Order Finite Volume IMEX
  Runge-Kutta Schemes for Two Dimensional Parabolic PDEs in Finance. Hyperbolic
  Problems: Theory, Numerics, Applications. SEMA SIMAI Springer Series, vol 35.
  Springer, Cham, 2024},
    year={2024},
    doi={10.1007/978-3-031-55264-9_13},
    archivePrefix={arXiv},
    eprint={2409.01131},
    primaryClass={math.NA cs.NA}
}