A meshless method in reproducing kernel space for solving variable-order time fractional advection-diffusion equations on arbitrary domain

DOI10.1016/j.aml.2020.107014zbMath1468.65172OpenAlexW3120841798MaRDI QIDQ2021481

Tiejun Yang, Hong Du, Zhong Chen

Publication date: 27 April 2021

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

Full work available at URL: https://doi.org/10.1016/j.aml.2020.107014

zbMATH Keywords

meshless methodadvection-diffusion equationMercer kernelreproducing kernel spacevariable-order time fractional differential equation

Mathematics Subject Classification ID

Numerical methods for partial differential equations, initial value and time-dependent initial-boundary value problems (65M99) Second-order parabolic equations (35K10) Fractional partial differential equations (35R11)

Related Items (13)

A new meshless method of solving 2D fractional diffusion-wave equations ⋮ The performance of a numerical scheme on the variable-order time-fractional advection-reaction-subdiffusion equations ⋮ A broken reproducing kernel method for the multiple interface problems ⋮ Higher Order Difference Operators and Associated Relative Reproducing Kernel Hilbert Spaces ⋮ A meshless method for solving two-dimensional distributed-order time-fractional cable equation ⋮ A novel meshless method based on RBF for solving variable-order time fractional advection-diffusion-reaction equation in linear or nonlinear systems ⋮ Meshfree methods for the variable-order fractional advection-diffusion equation ⋮ Reproducing kernel functions based univariate spline interpolation ⋮ On a collocation point of view to reproducing kernel methods ⋮ Local discontinuous Galerkin method for multi-term variable-order time fractional diffusion equation ⋮ Adaptive meshless numerical method of solving 2D variable order time fractional mobile-immobile advection-diffusion equations ⋮ Lobatto-reproducing kernel method for solving a linear system of second order boundary value problems ⋮ An efficient method based on least-squares technique for interface problems

Cites Work

• Eigenvalues of integral operators defined by smooth positive definite kernels
• A meshless method for solving two-dimensional variable-order time fractional advection-diffusion equation
• A least square point of view to reproducing kernel methods to solve functional equations
• A new reproducing kernel method with higher convergence order for solving a Volterra-Fredholm integral equation
• A stable least residue method in reproducing kernel space for solving a nonlinear fractional integro-differential equation with a weakly singular kernel
• A fourth-order least-squares based reproducing kernel method for one-dimensional elliptic interface problems
• Exact solution of a class of fractional integro‐differential equations with the weakly singular kernel based on a new fractional reproducing kernel space
• Theory of Reproducing Kernels
• Scattered Data Approximation

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