An Efficient Higher-Order Numerical Scheme for Solving Fractional Black-Scholes PDE Using Analytical Weights

Dai, Xiurong; Ullah, Malik Zaka

doi:10.1007/s40995-024-01588-x

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A Pde Problem1

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2024

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“…It is observed that Equation (45) simplifies to the classical Black-Scholes partial differential equation (BS PDE) when H = 1/2. If we designate E as the price of the strike, the initial condition for (45) can alternatively be characterized for the call and put variations [27,28]:…”

Section: A Pde Problemmentioning

confidence: 99%

Efficient Fourth-Order Weights in Kernel-Type Methods without Increasing the Stencil Size with an Application in a Time-Dependent Fractional PDE Problem

Liu,

Shateyi

2024

Mathematics

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An effective strategy to enhance the convergence order of nodal approximations in interpolation or PDE problems is to increase the size of the stencil, albeit at the cost of increased computational burden. In this study, our goal is to improve the convergence orders for approximating the first and second derivatives of sufficiently differentiable functions using the radial basis function-generated Hermite finite-difference (RBF-HFD) scheme. By utilizing only three equally spaced points in 1D, we are able to boost the convergence rate to four. Extensive tests have been conducted to demonstrate the effectiveness of the proposed theoretical weighting coefficients in solving interpolation and PDE problems.

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Section: A Pde Problemmentioning

confidence: 99%