Novel spectral schemes to fractional problems with nonsmooth solutions

DOI10.1002/mma.9343zbMath1530.65080OpenAlexW4372317553MaRDI QIDQ6185463

Waleed M. Abd-Elhameed, Glalal M. Moatimid, A. G. Atta, Youssri H. Youssri

Publication date: 8 January 2024

Published in: Mathematical Methods in the Applied Sciences (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1002/mma.9343

zbMATH Keywords

convergence analysisspectral methodsfractional initial-value problemChebyshev polynomials of the fifth kindtime-fractional partial differential problem

Mathematics Subject Classification ID

Stability and convergence of numerical methods for ordinary differential equations (65L20) Finite element, Rayleigh-Ritz, Galerkin and collocation methods for ordinary differential equations (65L60) Error bounds for numerical methods for ordinary differential equations (65L70)

Cites Work

• Unnamed Item
• Unnamed Item
• Fractional Sturm-Liouville eigen-problems: theory and numerical approximation
• Exponentially accurate spectral and spectral element methods for fractional ODEs
• High-order finite element methods for time-fractional partial differential equations
• Recent applications of fractional calculus to science and engineering
• On Mittag-Leffler-type functions in fractional evolution processes
• Generalized Fibonacci operational collocation approach for fractional initial value problems
• Fifth-kind orthonormal Chebyshev polynomial solutions for fractional differential equations
• Shifted fifth-kind Chebyshev Galerkin treatment for linear hyperbolic first-order partial differential equations
• Identifying the space source term problem for a generalization of the fractional diffusion equation with hyper-Bessel operator
• Spectral Galerkin treatment of linear one-dimensional telegraph type problem via the generalized Lucas polynomials
• Mild solutions to a time-fractional Cauchy problem with nonlocal nonlinearity in Besov spaces
• On backward problems for stochastic fractional reaction equations with standard and fractional Brownian motion
• Bivariate Chebyshev polynomials of the fifth kind for variable-order time-fractional partial integro-differential equations with weakly singular kernel
• Operational matrices based on the shifted fifth-kind Chebyshev polynomials for solving nonlinear variable order integro-differential equations
• On fractional-Legendre spectral Galerkin method for fractional Sturm-Liouville problems
• A fast element-free Galerkin method for the fractional diffusion-wave equation
• Semi-implicit Galerkin-Legendre spectral schemes for nonlinear time-space fractional diffusion-reaction equations with smooth and nonsmooth solutions
• Fully discrete spectral methods for solving time fractional nonlinear sine-Gordon equation with smooth and non-smooth solutions
• A novel spectral Galerkin/Petrov-Galerkin algorithm for the multi-dimensional space-time fractional advection-diffusion-reaction equations with nonsmooth solutions
• Generalized Lucas polynomial sequence treatment of fractional pantograph differential equation
• On Cauchy problem for fractional parabolic-elliptic Keller-Segel model
• Sharp Error Bounds for Jacobi Expansions and Gegenbauer--Gauss Quadrature of Analytic Functions
• Spectral Methods
• A Spectral Method (of Exponential Convergence) for Singular Solutions of the Diffusion Equation with General Two-Sided Fractional Derivative
• A Space-Time Petrov-Galerkin Spectral Method for Time Fractional Fokker-Planck Equation with Nonsmooth Solution
• A Novel Numerical Approach to Time-Fractional Parabolic Equations with Nonsmooth Solutions
• A new efficient algorithm based on fifth-kind Chebyshev polynomials for solving multi-term variable-order time-fractional diffusion-wave equation
• On the initial value problem for a class of nonlinear biharmonic equation with time-fractional derivative
• Error Analysis of a Finite Difference Method on Graded Meshes for a Time-Fractional Diffusion Equation
• Existence and regularity results for terminal value problem for nonlinear fractional wave equations
• Shifted Gegenbauer-Gauss Collocation Method for Solving Fractional Neutral Functional-Differential Equations with Proportional Delays

This page was built for publication: Novel spectral schemes to fractional problems with nonsmooth solutions