An efficient ADI difference scheme for the nonlocal evolution problem in three-dimensional space

H Zhang, Y Liu, X Yang - Journal of Applied Mathematics and Computing, 2023 - Springer
This paper addresses the numerical solution of the three-dimensional nonlocal evolution
equation with a weakly singular kernel. The first order fractional convolution quadrature …

Fast BDF2 ADI methods for the multi-dimensional tempered fractional integrodifferential equation of parabolic type

L Qiao, J Guo, W Qiu - Computers & Mathematics with Applications, 2022 - Elsevier
In this paper, we consider the numerical solutions of the multi-dimensional tempered
fractional integrodifferential equation. First, the second-order backward differentiation …

A second-order ADI difference scheme based on non-uniform meshes for the three-dimensional nonlocal evolution problem

L Qiao, W Qiu, D Xu - Computers & Mathematics with Applications, 2021 - Elsevier
This work constructs and analyzes a nonlocal evolution equation with a weakly singular
kernel in three-dimensional space. In the temporal direction, the Crank-Nicolson (CN) …

A fast ADI orthogonal spline collocation method with graded meshes for the two-dimensional fractional integro-differential equation

L Qiao, D Xu - Advances in Computational Mathematics, 2021 - Springer
We propose and analyze a time-stepping Crank-Nicolson (CN) alternating direction implicit
(ADI) scheme combined with an arbitrary-order orthogonal spline collocation (OSC) …

Discrete L1 remainder stability of first and second order schemes for a Volterra integro-differential equation

W Qiu, Y Chen, X Xiao, X Zheng - Mathematics and Computers in …, 2024 - Elsevier
This work investigates the discrete L 1 remainder stability of first and second order schemes
for a Volterra integro-differential equation, where the backward Euler and backward …

Finite Element Approximation for the Delayed Generalized Burgers–Huxley Equation with Weakly Singular Kernel: Part II Nonconforming and DG Approximation

S Mahahjan, A Khan - SIAM Journal on Scientific Computing, 2024 - SIAM
In this paper, the numerical approximation of the generalized Burgers–Huxley equation
(GBHE) with weakly singular kernels using nonconforming methods will be presented …

An hp-version fractional collocation method for Volterra integro-differential equations with weakly singular kernels

Z Ma, C Huang - Numerical Algorithms, 2023 - Springer
In this paper, we propose an hp-version fractional collocation method for solving second
kind Volterra integro-differential equations with weakly singular kernels. We derive hp …

[PDF][PDF] Nonpolynomial Jacobi spectral-collocation method for weakly singular Fredholm integral equations of the second kind

Q Huang, M Wang - Adv. Appl. Math. Mech., 2024 - global-sci.com
In this paper a nonpolynomial Jacobi spectral-collocation (NJSC) method for the second
kind Fredholm integral equations (FIEs) with weakly singular kernel| s− t|− γ is proposed. By …

A fast numerical solution of the 3D nonlinear tempered fractional integrodifferential equation

L Qiao, W Qiu, B Tang - Numerical Methods for Partial …, 2023 - Wiley Online Library
In this paper, we investigate the numerical solution of the three‐dimensional (3D) nonlinear
tempered fractional integrodifferential equation which is subject to the initial and boundary …

A fractional order collocation method for second kind Volterra integral equations with weakly singular kernels

H Cai, Y Chen - Journal of Scientific Computing, 2018 - Springer
In this paper, we develop a fractional order spectral collocation method for solving second
kind Volterra integral equations with weakly singular kernels. It is well known that the …