The implicit midpoint method for Riesz tempered fractional diffusion equation with a nonlinear source term

DOI10.1186/s13662-019-1990-yzbMath1458.65108OpenAlexW2923523718MaRDI QIDQ667961

Xuenian Cao, Dongdong Hu

Publication date: 4 March 2019

Published in: Advances in Difference Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1186/s13662-019-1990-y

zbMATH Keywords

stabilityconvergenceimplicit midpoint methodRiesz tempered fractional diffusion equation

Mathematics Subject Classification ID

Processes with independent increments; Lévy processes (60G51) Heat equation (35K05) Finite difference methods for initial value and initial-boundary value problems involving PDEs (65M06) Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12) Fractional partial differential equations (35R11)

Related Items (2)

Second-order numerical methods for the tempered fractional diffusion equations ⋮ A numerical algorithm for the Caputo tempered fractional advection-diffusion equation

Uses Software

• TFPDE

Cites Work

• High order schemes for the tempered fractional diffusion equations
• Third order difference schemes (without using points outside of the domain) for one sided space tempered fractional partial differential equations
• Tempered fractional calculus
• Crank-Nicolson method for the fractional diffusion equation with the Riesz fractional derivative
• An implicit midpoint difference scheme for the fractional Ginzburg-Landau equation
• Tempered stable Lévy motion and transient super-diffusion
• Stability and convergence of the Crank-Nicolson scheme for a class of variable-coefficient tempered fractional diffusion equations
• Generalized B-splines' geometric iterative fitting method with mutually different weights
• High-order numerical algorithms for Riesz derivatives via constructing new generating functions
• High-order quasi-compact difference schemes for fractional diffusion equations
• Finite element solutions for the space fractional diffusion equation with a nonlinear source term
• A finite difference/finite element technique with error estimate for space fractional tempered diffusion-wave equation
• Finite element method for a symmetric tempered fractional diffusion equation
• The numerical simulation of the tempered fractional Black-Scholes equation for European double barrier option
• Circulant preconditioning technique for barrier options pricing under fractional diffusion models
• Second-order BDF time approximation for Riesz space-fractional diffusion equations
• The restaurant at the end of the random walk: recent developments in the description of anomalous transport by fractional dynamics
• Stochastic Volatility for Lévy Processes
• Fractional differentiation matrices with applications
• High Order Algorithms for the Fractional Substantial Diffusion Equation with Truncated Lévy Flights
• Numerical Methods for SPDEs with Tempered Stable Processes
• Tempered Fractional Sturm--Liouville EigenProblems

This page was built for publication: The implicit midpoint method for Riesz tempered fractional diffusion equation with a nonlinear source term