Kernel-based approximation for Cauchy problem of the time-fractional diffusion equation

DOI10.1016/j.enganabound.2012.03.003zbMath1352.65309OpenAlexW2005407058MaRDI QIDQ2520194

Fang-Fang Dou, Benny Y. C. Hon

Publication date: 13 December 2016

Published in: Engineering Analysis with Boundary Elements (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.enganabound.2012.03.003

zbMATH Keywords

fundamental solutioninverse Laplace transformTikhonov regularization\(L\)-curvekernel-based approximationCauchy problem of time-fractional diffusion equation

Mathematics Subject Classification ID

Integro-partial differential equations (45K05) Laplace transform (44A10) Numerical methods for inverse problems for initial value and initial-boundary value problems involving PDEs (65M32) Fractional partial differential equations (35R11)

Related Items

Solving fractional optimal control problems within a Chebyshev–Legendre operational technique, The simplified Tikhonov regularization method for solving a Riesz-Feller space-fractional backward diffusion problem, Efficient Kansa-type MFS algorithm for time-fractional inverse diffusion problems, Meshless analyses for time-fractional heat diffusion in functionally graded materials, The MFS and MAFS for solving Laplace and biharmonic equations, An extension of the singular boundary method for solving two dimensional time fractional diffusion equations, Analysis of 3D transient heat conduction in functionally graded materials using a local semi-analytical space-time collocation scheme, State parametrization method based on shifted Legendre polynomials for solving fractional optimal control problems, A quasi-reversibility method for solving a two-dimensional time-fractional inverse heat conduction problem, Modeling and simulation of the fractional space-time diffusion equation, Reconstruction of the Robin boundary condition and order of derivative in time fractional heat conduction equation, A mollification regularization method for a fractional-diffusion inverse heat conduction problem, Numerical computation for backward time-fractional diffusion equation, A Kansa-type MFS scheme for two-dimensional time fractional diffusion equations, Source identification problems for radially symmetric and axis-symmetric heat conduction equations, A Localized Space-Time Method of Fundamental Solutions for Diffusion and Convection-Diffusion Problems, Fundamental kernel-based method for backward space-time fractional diffusion problem, Derivation and numerical validation of the fundamental solutions for constant and variable-order structural derivative advection-dispersion models, Reconstruction Robin Boundary Condition in the Heat Conduction Inverse Problem of Fractional Order, A modified Tikhonov regularization method for a Cauchy problem of a time fractional diffusion equation, The method of fundamental solution for the inverse source problem for the space-fractional diffusion equation, Convexity and solvability for compactly supported radial basis functions with different shapes, A numerical technique based on the shifted Legendre polynomials for solving the time-fractional coupled KdV equations

Uses Software

• Matlab
• Regularization tools
• Mittag-Leffler

Cites Work

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