Chebyshev polynomials of sixth kind for solving nonlinear fractional PDEs with proportional delay and its convergence analysis
type: Item
instance of: scholarly article
title: Chebyshev polynomials of sixth kind for solving nonlinear fractional PDEs with proportional delay and its convergence analysis
DOI: 10.1155/2022/9512048
author: Khadijeh Sadri
author: Hossein Aminikhah
published in: Journal of Function Spaces
publication date: 2022-01-31T00:00:00Z
review text: Summary: This work devotes to solving a class of delay fractional partial differential equations that arises in physical, biological, medical, and climate models. For this, a numerical scheme is implemented that applies operational matrices to convert the main problem into a system of algebraic equations; then, solving the resultant system leads to an approximate solution. The two-variable Chebyshev polynomials of the sixth kind, as basis functions in the proposed method, are constructed by the one-variable ones, and their operational matrices are derived. Error bounds of approximate solutions and their fractional and classical derivatives are computed. With the aid of these bounds, a bound for the residual function is estimated. Three illustrative examples demonstrate the simplicity and efficiency of the proposed method.
Mathematics Subject Classification ID: 65-XX
Mathematics Subject Classification ID: 35R11
zbMATH DE Number: 7466798
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2022/9512048
OpenAlex ID: W4206498263
Wikidata QID: Q114067410
cites work: Theory and applications of partial functional differential equations
cites work: Solution of delay differential equations via a homotopy perturbation method
cites work: Functional constraints method for constructing exact solutions to delay reaction-diffusion equations and more complex nonlinear equations
cites work: A numerical solution for a class of time fractional diffusion equations with delay
cites work: Convergence and stability estimates in difference setting for time‐fractional parabolic equations with functional delay
cites work: A general framework for the numerical analysis of high-order finite difference solvers for nonlinear multi-term time-space fractional partial differential equations with time delay
cites work: Numerical solution of non-linear fourth order fractional sub-diffusion wave equation with time delay
cites work: An integral formula for generalized Gegenbauer polynomials and Jacobi polynomials
cites work: Markov-Bernstein inequalities for generalized Gegenbauer weight
cites work: A class of Sobolev orthogonal polynomials on the unit circle and associated continuous dual Hahn polynomials: bounds, asymptotics and zeros
cites work: Asymptotic expansions of Jacobi polynomials and of the nodes and weights of Gauss-Jacobi quadrature for large degree and parameters in terms of elementary functions
cites work: A fast numerical algorithm based on the second kind Chebyshev polynomials for fractional integro-differential equations with weakly singular kernels
cites work: Legendre orthogonal polynomial method in calculating reflection and transmission coefficients of fluid-loaded functionally gradient plates
cites work: Sixth-kind Chebyshev spectral approach for solving fractional differential equations
cites work: Shifted fifth-kind Chebyshev Galerkin treatment for linear hyperbolic first-order partial differential equations
cites work: Numerical solution of variable order fractional nonlinear quadratic integro-differential equations based on the sixth-kind Chebyshev collocation method
cites work: Bivariate Chebyshev polynomials of the fifth kind for variable-order time-fractional partial integro-differential equations with weakly singular kernel
cites work: A new efficient algorithm based on fifth-kind Chebyshev polynomials for solving multi-term variable-order time-fractional diffusion-wave equation
cites work: Numerical solution of time-fractional nonlinear PDEs with proportional delays by homotopy perturbation method
cites work: Q4250595
cites work: Jacobi approximations in non-uniformly Jacobi-weighted Sobolev spaces
cites work: New formulas of the high-order derivatives of fifth-kind Chebyshev polynomials: spectral solutionof the convection-diffusion equation
Recommended article: Sixth-kind Chebyshev spectral approach for solving fractional differential equations
Recommended article: Q5175736
Recommended article: Chebyshev polynomials approach for numerically solving system of two-dimensional fractional PDEs and convergence analysis
Recommended article: Generalized shifted Chebyshev polynomials: solving a general class of nonlinear variable order fractional PDE
Recommended article: Fractional Chebyshev Finite Difference Method for Solving the Fractional-Order Delay BVPs
Recommended article: On Chebyshev-Halley methods with sixth-order convergence for solving non-linear equations
Recommended article: Numerical solution of variable order fractional nonlinear quadratic integro-differential equations based on the sixth-kind Chebyshev collocation method
Recommended article: A new Chebyshev polynomial approximation for solving delay differential equations
Recommended article: Fifth-kind orthonormal Chebyshev polynomial solutions for fractional differential equations
Recommended article: Second kind shifted Chebyshev polynomials for solving space fractional order diffusion equation
description: scientific article; zbMATH DE number 7466798