Uniform convergence of V-cycle multigrid algorithms for two-dimensional fractional Feynman-Kac equation

DOI10.1007/s10915-017-0480-1zbMath1397.65177arXiv1602.08226OpenAlexW2623360684MaRDI QIDQ1742680

Weihua Deng, Minghua Chen, Stefano Serra Capizzano

Publication date: 12 April 2018

Published in: Journal of Scientific Computing (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1602.08226

zbMATH Keywords

uniform convergencefractional Feynman-Kac equationV-cycle multigrid methodToeplitz block tridiagonal matrix

Mathematics Subject Classification ID

Multigrid methods; domain decomposition for initial value and initial-boundary value problems involving PDEs (65M55) Toeplitz, Cauchy, and related matrices (15B05) Fractional partial differential equations (35R11)

Related Items (6)

Convergence Analysis of a Multigrid Method for a Nonlocal Model ⋮ A fast second-order scheme for nonlinear Riesz space-fractional diffusion equations ⋮ A Multigrid Method for Nonlocal Problems: Non--Diagonally Dominant or Toeplitz-Plus-Tridiagonal Systems ⋮ An efficient multigrid solver for two-dimensional spatial fractional diffusion equations with variable coefficients ⋮ Uniform convergence of V-cycle multigrid finite element method for one-dimensional time-dependent fractional problem ⋮ Numerical algorithms of the two-dimensional Feynman-Kac equation for reaction and diffusion processes

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Multigrid method for fractional diffusion equations
• Second-order LOD multigrid method for multidimensional Riesz fractional diffusion equation
• On distributions of functionals of anomalous diffusion paths
• A \(V\)-cycle multigrid for multilevel matrix algebras: proof of optimality
• A high-order compact finite difference scheme for the fractional sub-diffusion equation
• Multigrid methods for Toeplitz matrices
• Convergence analysis of two-grid methods for elliptic Toeplitz and PDEs matrix-sequences
• Generalized grid transfer operators for multigrid methods applied on Toeplitz matrices
• Numerical algorithms for the forward and backward fractional Feynman-Kac equations
• An algebraic generalization of local Fourier analysis for grid transfer operators in multigrid based on Toeplitz matrices
• Convergence Estimates for Multigrid Algorithms without Regularity Assumptions
• Sharp Estimates for Multigrid Rates of Convergence with General Smoothing and Acceleration
• New Convergence Estimates for Multigrid Algorithms
• A Review on the Inverse of Symmetric Tridiagonal and Block Tridiagonal Matrices
• The method of alternating projections and the method of subspace corrections in Hilbert space
• Multigrid Method for Ill-Conditioned Symmetric Toeplitz Systems
• V-cycle Optimal Convergence for Certain (Multilevel) Structured Linear Systems
• A Space-Time Multigrid Method for Parabolic Partial Differential Equations
• Multigrid Methods for Symmetric Positive Definite Block Toeplitz Matrices with Nonnegative Generating Functions
• Discretized fractional substantial calculus
• Fourth Order Accurate Scheme for the Space Fractional Diffusion Equations
• High Order Algorithms for the Fractional Substantial Diffusion Equation with Truncated Lévy Flights
• Fourth Order Difference Approximations for Space Riemann-Liouville Derivatives Based on Weighted and Shifted Lubich Difference Operators
• An Introduction to Iterative Toeplitz Solvers
• The Mathematical Theory of Finite Element Methods

This page was built for publication: Uniform convergence of V-cycle multigrid algorithms for two-dimensional fractional Feynman-Kac equation