The spectral meshless radial point interpolation method for solving an inverse source problem of the time-fractional diffusion equation

DOI10.1016/j.apnum.2018.02.008zbMath1462.65134OpenAlexW2794143476MaRDI QIDQ1748047

Ahmad Jafarabadi, Elyas Shivanian

Publication date: 2 May 2018

Published in: Applied Numerical Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.apnum.2018.02.008

zbMATH Keywords

regularizationradial basis functioninverse source problemfractional diffusion equationspectral meshless radial point interpolation (SMRPI) method

Mathematics Subject Classification ID

Smoothness and regularity of solutions to PDEs (35B65) Finite difference methods for initial value and initial-boundary value problems involving PDEs (65M06) Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs (65M70) PDEs with randomness, stochastic partial differential equations (35R60) Numerical methods for inverse problems for initial value and initial-boundary value problems involving PDEs (65M32) Fractional partial differential equations (35R11) Numerical radial basis function approximation (65D12)

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Cites Work

• Unnamed Item
• Unnamed Item
• Recent advances on radial basis function collocation methods
• An inverse problem for fractional diffusion equation in 2-dimensional case: stability analysis and regularization
• An inverse source problem in a semilinear time-fractional diffusion equation
• Numerical simulation of two-dimensional sine-Gordon solitons via a local weak meshless technique based on the radial point interpolation method (RPIM)
• A new regularization method for solving a time-fractional inverse diffusion problem
• Determination of an unknown source term and the temperature distribution for the linear heat equation involving fractional derivative in time
• Identification and regularization for unknown source for a time-fractional diffusion equation
• Spectral regularization method for solving a time-fractional inverse diffusion problem
• Meshless local Petrov-Galerkin (MLPG) method for the unsteady magnetohydrodynamic (MHD) flow through pipe with arbitrary wall conductivity
• Diffusion subject to the specification of mass
• Generalizing the finite element method: Diffuse approximation and diffuse elements
• Numerical solution of the space fractional Fokker-Planck equation.
• Meshless local Petrov-Galerkin (MLPG) method for three-dimensional nonlinear wave equations via moving least squares approximation
• A meshless technique based on the local radial basis functions collocation method for solving parabolic-parabolic Patlak-Keller-Segel chemotaxis model
• Method of approximate particular solutions for constant- and variable-order fractional diffusion models
• The meshless local collocation method for solving multi-dimensional Cahn-Hilliard, Swift-Hohenberg and phase field crystal equations
• Analysis of the spectral meshless radial point interpolation for solving fractional reaction-subdiffusion equation
• A new spectral meshless radial point interpolation (SMRPI) method: a well-behaved alternative to the meshless weak forms
• Solution for a fractional diffusion-wave equation defined in a bounded domain
• Finite difference approximations for fractional advection-dispersion flow equations
• An iteration regularization for a time-fractional inverse diffusion problem
• Two regularization methods to identify a space-dependent source for the time-fractional diffusion equation
• A fractional diffusion equation to describe Lévy flights
• A modified kernel method for a time-fractional inverse diffusion problem
• Comparison between two meshless methods based on collocation technique for the numerical solution of four-species tumor growth model
• Inverse source problem for a time-fractional diffusion equation with nonlocal boundary conditions
• Regularized solution of an inverse source problem for a time fractional diffusion equation
• An improved spectral meshless radial point interpolation for a class of time-dependent fractional integral equations: 2D fractional evolution equation
• Finite difference/spectral approximations for the time-fractional diffusion equation
• Time fractional IHCP with Caputo fractional derivatives
• Variational multiscale element free Galerkin (VMEFG) and local discontinuous Galerkin (LDG) methods for solving two-dimensional Brusselator reaction-diffusion system with and without cross-diffusion
• A modified quasi-boundary value method for an inverse source problem of the time-fractional diffusion equation
• Analysis of meshless local radial point interpolation (MLRPI) on a nonlinear partial integro-differential equation arising in population dynamics
• Stable numerical solution of a fractional-diffusion inverse heat conduction problem
• Reconstruction of a time-dependent source term in a time-fractional diffusion equation
• On the convergence analysis, stability, and implementation of meshless local radial point interpolation on a class of three-dimensional wave equations
• A Primer on Radial Basis Functions with Applications to the Geosciences
• Uniqueness in an inverse problem for a one-dimensional fractional diffusion equation
• A Galerkin Procedure for the Diffusion Equation Subject to the Specification of Mass
• Existence of A Solution to The N Dimensional Problem of Thermoelastic Contact
• A Boundary Meshless Method for Solving Heat Transfer Problems Using the Fourier Transform
• Solving PDEs with radial basis functions
• Theoretical Numerical Analysis
• Error and stability analysis of numerical solution for the time fractional nonlinear Schrödinger equation on scattered data of general‐shaped domains
• A boundary value problem in the theory of heat conduction with a nonclassical boundary condition

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