Advanced shifted sixth-kind Chebyshev tau approach for solving linear one-dimensional hyperbolic telegraph type problem

DOI10.1007/s40096-022-00460-6OpenAlexW4220899192WikidataQ115600748 ScholiaQ115600748MaRDI QIDQ6066831

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

Publication date: 14 December 2023

Published in: Mathematical Sciences (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s40096-022-00460-6

zbMATH Keywords

convergence analysishypergeometric functionsspectral methodshyperbolic telegraph equationKronecker algebraChebyshev polynomials of the sixth-kind

Mathematics Subject Classification ID

Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs (65M70) Special sequences and polynomials (11B83) First-order hyperbolic equations (35L02)

Related Items (1)

Evaluating the impacts of thermal conductivity on Casson fluid flow near a slippery sheet: numerical simulation using sixth-kind Chebyshev polynomials

Cites Work

• The solution of a time-dependent problem by the \(B\)-spline method
• Accurate spectral solutions for the parabolic and elliptic partial differential equations by the ultraspherical tau method
• On the coefficients of differentiated expansions and derivatives of Chebyshev polynomials of the third and fourth kinds
• Numerical time-dependent partial differential equations for scientists and engineering.
• A new operational matrix of Caputo fractional derivatives of Fermat polynomials: an application for solving the Bagley-Torvik equation
• Generalized Fibonacci operational collocation approach for fractional initial value problems
• Sixth-kind Chebyshev spectral approach for solving fractional differential equations
• An integral formula for generalized Gegenbauer polynomials and Jacobi polynomials
• Fifth-kind orthonormal Chebyshev polynomial solutions for fractional differential equations
• A spatial-temporal GFDM with an additional condition for transient heat conduction analysis of FGMs
• Shifted fifth-kind Chebyshev Galerkin treatment for linear hyperbolic first-order partial differential equations
• A GFDM with supplementary nodes for thin elastic plate bending analysis under dynamic loading
• Numerical solution for the time-fractional Fokker-Planck equation via shifted Chebyshev polynomials of the fourth kind
• Neoteric formulas of the monic orthogonal Chebyshev polynomials of the sixth-kind involving moments and linearization formulas
• Numerical study of multi-dimensional hyperbolic telegraph equations arising in nuclear material science via an efficient local meshless method
• On the numerical solution of Fisher's equation by an efficient algorithm based on multiwavelets
• Haar wavelet collocation method for solving singular and nonlinear fractional time-dependent Emden-Fowler equations with initial and boundary conditions
• Exponential Jacobi spectral method for hyperbolic partial differential equations
• Shifted-Chebyshev-polynomial-based numerical algorithm for fractional order polymer visco-elastic rotating beam
• A hybrid meshless method for the solution of the second order hyperbolic telegraph equation in two space dimensions
• Exponential Jacobi-Galerkin method and its applications to multidimensional problems in unbounded domains
• Modified variational iteration algorithm-II: convergence and applications to diffusion models
• A novel approach for solving an inverse reaction-diffusion-convection problem
• Lagrange's operational approach for the approximate solution of two-dimensional hyperbolic telegraph equation subject to Dirichlet boundary conditions
• Solving the telegraph equation in 2-d and 3-d using generalized finite difference method (GFDM)
• An innovative harmonic numbers operational matrix method for solving initial value problems
• Hypergeometric summation. An algorithmic approach to summation and special function identities
• Hypergeometric fractional derivatives formula of shifted Chebyshev polynomials: tau algorithm for a type of fractional delay differential equations
• Matrix Algorithms
• A method based on meshless approach for the numerical solution of the two-space dimensional hyperbolic telegraph equation
• Numerical solution of hyperbolic telegraph equation using the Chebyshev tau method
• A numerical method for solving the hyperbolic telegraph equation
• A numerical scheme based on Bernoulli wavelets and collocation method for solving fractional partial differential equations with Dirichlet boundary conditions
• A robust spectral treatment of a class of initial value problems using modified Chebyshev polynomials
• Integrating Krylov Deferred Correction and Generalized Finite Difference Methods for Dynamic Simulations of Wave Propagation Phenomena in Long-Time Intervals
• Fully Legendre Spectral Galerkin Algorithm for Solving Linear One-Dimensional Telegraph Type Equation
• New Tchebyshev‐Galerkin operational matrix method for solving linear and nonlinear hyperbolic telegraph type equations
• A Haar wavelet collocation approach for solving one and two‐dimensional second‐order linear and nonlinear hyperbolic telegraph equations

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