Numerical approximation of the nonlinear time-fractional telegraph equation arising in neutron transport

DOI10.1016/j.cnsns.2021.105755zbMath1471.65162OpenAlexW3127534953MaRDI QIDQ2025507

Zakieh Avazzadeh, Omid Nikan, José António Tenreiro Machado

Publication date: 14 May 2021

Published in: Communications in Nonlinear Science and Numerical Simulation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.cnsns.2021.105755

zbMATH Keywords

RBFstabilityconvergenceCaputo fractional derivativefractional telegraph equationLRBF-FD

Mathematics Subject Classification ID

Finite difference methods for initial value and initial-boundary value problems involving PDEs (65M06) Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12) Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs (65M70) Finite difference methods for boundary value problems involving PDEs (65N06) Nuclear reactor theory; neutron transport (82D75) Fractional partial differential equations (35R11) Numerical radial basis function approximation (65D12)

Related Items (35)

Meshless approach to the large-eddy simulation of the continuous casting process ⋮ Numerical simulation of a degenerate parabolic problem occurring in the spatial diffusion of biological population ⋮ Solution of non-linear time fractional telegraph equation with source term using B-spline and Caputo derivative ⋮ On the use of an accurate implicit spectral approach for the telegraph equation in propagation of electrical signals ⋮ Numerical study of nonlinear generalized Burgers-Huxley equation by multiquadric quasi-interpolation and pseudospectral method ⋮ Novel and accurate Gegenbauer spectral tau algorithms for distributed order nonlinear time-fractional telegraph models in multi-dimensions ⋮ The finite difference method for the fourth‐order partial integro‐differential equations with the multi‐term weakly singular kernel ⋮ Alternating direction implicit approach for the two-dimensional time fractional nonlinear Klein-Gordon and sine-Gordon problems ⋮ Application of Pell collocation method for solving the general form of time-fractional Burgers equations ⋮ An RBF-FD method for the time-fractional advection-dispersion equation with nonlinear source term ⋮ A high-order unconditionally stable numerical method for a class of multi-term time-fractional diffusion equation arising in the solute transport models ⋮ A novel linearized Galerkin finite element scheme with fractional Crank–Nicolson method for the nonlinear coupled delay subdiffusion system with smooth solutions ⋮ Reproducing kernel method to solve non-local fractional boundary value problem ⋮ Unnamed Item ⋮ An efficient alternating direction implicit finite difference scheme for the three-dimensional time-fractional telegraph equation ⋮ Numerical approach for modeling fractional heat conduction in porous medium with the generalized Cattaneo model ⋮ Unnamed Item ⋮ A robust computational framework for analyzing the Bloch-Torrey equation of fractional order ⋮ An existence result for an infinite system of implicit fractional integral equations via generalized Darbo's fixed point theorem ⋮ Qualitative analysis of Caputo fractional integro-differential equations with constant delays ⋮ Coupling of the Crank-Nicolson scheme and localized meshless technique for viscoelastic wave model in fluid flow ⋮ Two spectral Legendre's derivative algorithms for Lane-Emden, Bratu equations, and singular perturbed problems ⋮ Numerical simulation of fractional evolution model arising in viscoelastic mechanics ⋮ Numerical solution using radial basis functions for multidimensional fractional partial differential equations of type Black-Scholes ⋮ On numerical simulations of time fractional phi-four equation using Caputo derivative ⋮ An efficient difference scheme for time-fractional KdV equation ⋮ On a high-order Gaussian radial basis function generated Hermite finite difference method and its application ⋮ Application of combination schemes based on radial basis functions and finite difference to solve stochastic coupled nonlinear time fractional sine-Gordon equations ⋮ Inverse problems for a multi-term time fractional evolution equation with an involution ⋮ Error analysis of fast L1 ADI finite difference/compact difference schemes for the fractional telegraph equation in three dimensions ⋮ Numerical analysis of time-fractional Sobolev equation for fluid-driven processes in impermeable rocks ⋮ Analytic solutions of fractal and fractional time derivative-Burgers-Nagumo equation ⋮ Spectral solutions with error analysis of Volterra-Fredholm integral equation via generalized Lucas collocation method ⋮ Numerical approximation of fractional telegraph equation via Legendre collocation technique ⋮ Boubaker polynomials and their applications for solving fractional two-dimensional nonlinear partial integro-differential Volterra integral equations

Uses Software

• Matlab

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Stability and convergence of finite difference schemes for a class of time-fractional sub-diffusion equations based on certain superconvergence
• A local radial basis function method for advection-diffusion-reaction equations on complexly shaped domains
• Theory and applications of the multiquadric-biharmonic method. 20 years of discovery 1968-1988
• Multiquadrics - a scattered data approximation scheme with applications to computational fluid-dynamics. I: Surface approximations and partial derivative estimates
• A numerical study of some radial basis function based solution methods for elliptic PDEs
• Representation of exact solution for the time-fractional telegraph equation in the reproducing kernel space
• Fractional derivatives for physicists and engineers. Volume I: Background and theory. Volume II: Applications
• Fractional generalization of memristor and higher order elements
• On using radial basis functions in a ``finite difference mode with applications to elasticity problems
• Numerical solution of time-fractional fourth-order reaction-diffusion model arising in composite environments
• Applied functional analysis. Functional analysis, Sobolev spaces and elliptic differential equations
• Convergence order estimates of meshless collocation methods using radial basis functions
• The fractional calculus. Theory and applications of differentiation and integration to arbitrary order
• An efficient numerical scheme for Burger equation
• Local radial basis function-based differential quadrature method and its application to solve two-dimensional incompressible Navier--Stokes equations
• Introduction to fractional differential equations
• Local integration of 2-D fractional telegraph equation via moving least squares approximation
• Using radial basis function-generated finite differences (RBF-FD) to solve heat transfer equilibrium problems in domains with interfaces
• Numerical methods for solving the time-fractional telegraph equation
• An improved tau method for the multi-dimensional fractional Rayleigh-Stokes problem for a heated generalized second grade fluid
• Wavelets method for solving fractional optimal control problems
• Fractional-order modeling of neutron transport in a nuclear reactor
• Multiquadrics -- a scattered data approximation scheme with applications to computational fluid-dynamics. II: Solutions to parabolic, hyperbolic and elliptic partial differential equations
• Error estimates and condition numbers for radial basis function interpolation
• Fractional nonlinear dynamics of learning with memory
• Generalized shifted Chebyshev polynomials: solving a general class of nonlinear variable order fractional PDE
• Derivation of the nonlocal pressure form of the fractional porous medium equation in the hydrological setting
• A numerical approach for solving fractional optimal control problems using modified hat functions
• Chebyshev cardinal wavelets and their application in solving nonlinear stochastic differential equations with fractional Brownian motion
• Numerical investigation of fractional nonlinear sine-Gordon and Klein-Gordon models arising in relativistic quantum mechanics
• A meshless method for time fractional nonlinear mixed diffusion and diffusion-wave equation
• On the stability of fractional neutron point kinetics (FNPK)
• Numerical solution of fractional telegraph equation by using radial basis functions
• A fully discrete difference scheme for a diffusion-wave system
• Scattered node compact finite difference-type formulas generated from radial basis functions
• Spectral meshless radial point interpolation (SMRPI) method to two-dimensional fractional telegraph equation
• The meshless method of radial basis functions for the numerical solution of time fractional telegraph equation
• Scattered Data Interpolation: Tests of Some Method
• Radial Basis Functions
• Multivariate Interpolation and Conditionally Positive Definite Functions. II
• Fast high order difference schemes for the time fractional telegraph equation
• Numerical scheme with convergence for a generalized time‐fractional Telegraph‐type equation

This page was built for publication: Numerical approximation of the nonlinear time-fractional telegraph equation arising in neutron transport