Numerical approximation and fast implementation to a generalized distributed-order time-fractional option pricing model

Zhang, Meihui; Jia, Jinhong; Zheng, Xiangcheng

doi:10.1016/j.chaos.2023.113353

Cited by 4 publications

(1 citation statement)

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“…ADI schemes for time fractional mobile-immobile linear and semi linear diffusion equations were proposed in [9,31]. Most recently, numerical schemes and analysis based on finite element method (FEM) were established in [19,35] for solving variable order time fractional option pricing models. A characteristic FEM for solving TFCDE was developed in [14].…”

Section: Introductionmentioning

confidence: 99%

A New Compact Numerical Scheme for Solving Time Fractional Mobile-Immobile Advection-Dispersion Model

Thomas,

Nadupuri

2023

MJMS

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This work is focused on the derivation and analysis of a novel numerical technique for solving time fractional mobile-immobile advection-dispersion equation which models many complex systems in engineering and science. The scheme is derived using the effective combination of Euler and Caputo numerical techniques for approximating the integer and fractional time derivatives respectively, and a fourth order exponential compact scheme for spatial derivatives. The Fourier analysis technique is used to prove that the proposed numerical scheme is unconditionally stable and perform convergence analysis. To assess the viability and accuracy of the proposed scheme, some numerical examples are demonstrated with constant as well as variable order time fractional derivatives for this model.

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