Spectral solutions for a class of nonlinear wave equations with Riesz fractional based on Legendre collocation technique
DOI10.1016/j.cam.2022.114970zbMath1505.65271OpenAlexW4310018766MaRDI QIDQ2112705
Mohamed A. Abdelkawy, E. M. Soluma, Ibrahim Al-Dayel, Dumitru Baleanu
Publication date: 11 January 2023
Published in: Journal of Computational and Applied Mathematics (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1016/j.cam.2022.114970
nonlinear wave equationsspectral collocation methodCaputo fractional derivativeRiesz fractionalshifted Legendre Gauss-Lobatto quadratureshifted Legendre Gauss-Radau quadrature
Nonlinear waves in solid mechanics (74J30) Fractional derivatives and integrals (26A33) Fourier series in special orthogonal functions (Legendre polynomials, Walsh functions, etc.) (42C10) Nonlinear constitutive equations for materials with memory (74D10) Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs (65M70) Numerical quadrature and cubature formulas (65D32) PDEs in connection with mechanics of deformable solids (35Q74) Fractional partial differential equations (35R11)
Cites Work
- Novel second-order accurate implicit numerical methods for the Riesz space distributed-order advection-dispersion equations
- An efficient Jacobi pseudospectral approximation for nonlinear complex generalized Zakharov system
- A Jacobi spectral collocation method for solving multi-dimensional nonlinear fractional sub-diffusion equations
- An improved collocation method for multi-dimensional space-time variable-order fractional Schrödinger equations
- Jacobi-Gauss-Lobatto collocation method for the numerical solution of \(1+1\) nonlinear Schrödinger equations
- High-order algorithms for Riesz derivative and their applications. II
- A fully spectral collocation approximation for multi-dimensional fractional Schrödinger equations
- A second order explicit finite difference method for the fractional advection diffusion equation
- An accurate space-time pseudospectral method for solving nonlinear multi-dimensional heat transfer problems
- Fractional Noether's theorem in the Riesz-Caputo sense
- Fractional variational problems with the Riesz-Caputo derivative
- Highly accurate numerical schemes for multi-dimensional space variable-order fractional Schrödinger equations
- Energy estimates for two-dimensional space-Riesz fractional wave equation
- Numerical methods for fractional partial differential equations with Riesz space fractional derivatives
- Fractional differential equations. An introduction to fractional derivatives, fractional differential equations, to methods of their solution and some of their applications
- A Legendre collocation method for distributed-order fractional optimal control problems
- Jacobi collocation approximation for solving multi-dimensional Volterra integral equations
- A numerical method for solving the two-dimensional distributed order space-fractional diffusion equation on an irregular convex domain
- A novel finite volume method for the Riesz space distributed-order diffusion equation
- Finite difference approximations for fractional advection-dispersion flow equations
- Modal Hermite spectral collocation method for solving multi-dimensional hyperbolic telegraph equations
- An explicit fourth-order energy-preserving scheme for Riesz space fractional nonlinear wave equations
- A spectral collocation technique for Riesz fractional Chen-Lee-Liu equation
- Solving a non-linear fractional convection-diffusion equation using local discontinuous Galerkin method
- Semi-discretized numerical solution for time fractional convection-diffusion equation by RBF-FD
- Sinc-Galerkin method for solving the time fractional convection-diffusion equation with variable coefficients
- Legendre-Chebyshev spectral collocation method for two-dimensional nonlinear reaction-diffusion equation with Riesz space-fractional
- Highly accurate technique for solving distributed-order time-fractional-sub-diffusion equations of fourth order
- A new WENO based Chebyshev spectral volume method for solving one- and two-dimensional conservation laws
- LDG approximation of a nonlinear fractional convection-diffusion equation using B-spline basis functions
- Lagrange's operational approach for the approximate solution of two-dimensional hyperbolic telegraph equation subject to Dirichlet boundary conditions
- Chaos in the fractional order nonlinear Bloch equation with delay
- A fast and efficient numerical approach for solving advection-diffusion equations by using hybrid functions
- An efficient finite volume method for nonlinear distributed-order space-fractional diffusion equations in three space dimensions
- An approximation scheme for the time fractional convection-diffusion equation
- Fractional-order Legendre-Laguerre functions and their applications in fractional partial differential equations
- A new method for converting boundary value problems for impulsive fractional differential equations to integral equations and its applications
- Convergence analysis of space-time Jacobi spectral collocation method for solving time-fractional Schrödinger equations
- Nonlinear Analysis - Theory and Methods
- Space–time Chebyshev spectral collocation method for nonlinear time‐fractional Burgers equations based on efficient basis functions
- A class of second order difference approximations for solving space fractional diffusion equations
- Efficient Legendre spectral tau algorithm for solving the two-sided space–time Caputo fractional advection–dispersion equation
- Solving fractional optimal control problems within a Chebyshev–Legendre operational technique
- Fractional variational calculus in terms of Riesz fractional derivatives
- Nature’s Patterns and the Fractional Calculus
- Fractional Calculus
- Tomorrow’s Dynamics
This page was built for publication: Spectral solutions for a class of nonlinear wave equations with Riesz fractional based on Legendre collocation technique
