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A novel banded preconditioner for coupled tempered fractional diffusion equation generated from the regime-switching CGMY model
With the growing popularity of the regime-switching Lévy processes model in option pricing, the coupled tempered fractional diffusion equation...
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A second-order finite difference scheme for nonlinear tempered fractional integrodifferential equations in three dimensions
In this paper, we provide a numerical solution for the nonlinear tempered fractional integrodifferential equation in three dimensions. We use the...
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Crank-Nicolson ADI finite difference/compact difference schemes for the 3D tempered integrodifferential equation associated with Brownian motion
This paper proposes and analyzes a tempered fractional integrodifferential equation in three-dimensional (3D) space. The Crank-Nicolson (CN) method...
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An implicit-explicit preconditioned direct method for pricing options under regime-switching tempered fractional partial differential models
Recently, fractional partial differential equations have been widely applied in option pricing problems, which better explains many important...
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Exact solution with existence and uniqueness conditions for multi-dimensional time-space tempered fractional diffusion-wave equation
In this paper, we investigate the existence and uniqueness of the multi-dimensional time-space tempered fractional diffusion-wave (TSTFDW) equation...
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Fast solution method and simulation for the 2D time-space fractional Black-Scholes equation governing European two-asset option pricing
Fractional Black-Scholes (FBS) equation has been widely applied in options pricing problems. However, most of the literatures focus on pricing the...
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A class of moving Kriging interpolation-based DQ methods to simulate multi-dimensional space Galilei invariant fractional advection-diffusion equation
The current work concerns to develop a new local meshless procedure to simulate the one-, two- and three-dimensional space Galilei invariant...
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A finite-difference procedure to solve weakly singular integro partial differential equation with space-time fractional derivatives
The main aim of the current paper is to propose an efficient numerical technique for solving space-time fractional partial weakly singular...
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Shifted fractional Legendre spectral collocation technique for solving fractional stochastic Volterra integro-differential equations
This paper presents a spectral collocation technique to solve fractional stochastic Volterra integro-differential equations (FSV-IDEs). The algorithm...
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A predictor–corrector scheme for the tempered fractional differential equations with uniform and non-uniform meshes
Tempered fractional derivatives and the corresponding tempered fractional differential equations have played a key role in physical science. In this...
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The conservative characteristic difference method and analysis for solving two-sided space-fractional advection-diffusion equations
In this paper, we propose and analyze the mass-conservative characteristic finite difference method for solving two-sided space-fractional...
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Fast numerical approximation for the space-fractional semilinear parabolic equations on surfaces
In this work, a fast numerical method is considered to solve the space-fractional semilinear parabolic equations on closed surfaces. It is a...
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Wavelet regularization strategy for the fractional inverse diffusion problem
This manuscript deals with an inverse fractional-diffusing problem, the time-fractional heat conduction equation, which is a physical model of a...
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Numerical study of the variable-order fractional version of the nonlinear fourth-order 2D diffusion-wave equation via 2D Chebyshev wavelets
In this article, the 2D Chebyshev wavelets (CWs) are used for designing a proper procedure to solve the variable-order (VO) fractional version of the...
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A fast temporal second-order compact ADI difference scheme for the 2D multi-term fractional wave equation
In this paper, a fast temporal second-order compact ADI scheme is proposed for the 2D time multi-term fractional wave equation. At the...
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Meshless upwind local radial basis function-finite difference technique to simulate the time- fractional distributed-order advection–diffusion equation
The main objective in this paper is to propose an efficient numerical formulation for solving the time-fractional distributed-order...
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Investigation of heat transport equation at the microscale via interpolating element-free Galerkin method
The current paper concerns to develop a new meshless numerical procedure to solve heat transport equation. For this aim, the Crank–Nicolson finite...
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Numerical simulations based on shifted second-order difference/finite element algorithms for the time fractional Maxwell’s system
In this article, mixed element algorithms with second-order time convergence results for the two-dimensional time fractional Maxwell’s equations in...
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Investigations on several high-order ADI methods for time-space fractional diffusion equation
The paper is devoted to the construction of high-precision unconditionally stable finite difference methods for solving time-space fractional...
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A computational study of variable coefficients fractional advection–diffusion–reaction equations via implicit meshless spectral algorithm
In this article, a meshless spectral radial point interpolation method is proposed for the numerical solutions of a class of time-fractional...
