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A highly accurate Jacobi collocation algorithm for systems of high‐order linear differential–difference equations with mixed initial conditions
Author(s) -
Bhrawy A. H.,
Doha E. H.,
Baleanu D.,
Hafez R. M.
Publication year - 2015
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.3277
Subject(s) - mathematics , orthogonal collocation , collocation method , collocation (remote sensing) , spectral method , convergence (economics) , interpolation (computer graphics) , gauss , differential equation , order of accuracy , jacobi polynomials , mathematical analysis , numerical analysis , numerical partial differential equations , orthogonal polynomials , ordinary differential equation , computer science , animation , physics , computer graphics (images) , quantum mechanics , machine learning , economics , economic growth
In this paper, a shifted Jacobi–Gauss collocation spectral algorithm is developed for solving numerically systems of high‐order linear retarded and advanced differential–difference equations with variable coefficients subject to mixed initial conditions. The spatial collocation approximation is based upon the use of shifted Jacobi–Gauss interpolation nodes as collocation nodes. The system of differential–difference equations is reduced to a system of algebraic equations in the unknown expansion coefficients of the sought‐for spectral approximations. The convergence is discussed graphically. The proposed method has an exponential convergence rate. The validity and effectiveness of the method are demonstrated by solving several numerical examples. Numerical examples are presented in the form of tables and graphs to make comparisons with the results obtained by other methods and with the exact solutions more easier. Copyright © 2015 John Wiley & Sons, Ltd.