Scopus İndeksli Yayınlar Koleksiyonu

Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/8651

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Author: search.filters.author.Doha, E. H.Subject: search.filters.subject.Shifted Jacobi Polynomials

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Now showing 1 - 4 of 4
  • Article
    Citation - WoS: 20
    Citation - Scopus: 19
    A Highly Accurate Jacobi Collocation Algorithm for Systems of High-Order Linear Differential-Difference Equations With Mixed Initial Conditions
    (Wiley, 2015) Doha, E. H.; Baleanu, D.; Hafez, R. M.; Bhrawy, A. H.
    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 (C) 2015 John Wiley & Sons, Ltd.
  • Article
    Citation - WoS: 19
    Citation - Scopus: 18
    Efficient Jacobi-Gauss Collocation Method for Solving Initial Value Problems of Bratu Type
    (Pleiades Publishing inc, 2013) Bhrawy, A. H.; Baleanu, D.; Hafez, R. M.; Doha, E. H.
    In this paper, we propose the shifted Jacobi-Gauss collocation spectral method for solving initial value problems of Bratu type, which is widely applicable in fuel ignition of the combustion theory and heat transfer. The spatial approximation is based on shifted Jacobi polynomials J(n)((alpha, beta))(x) with alpha, beta is an element of (-1, infinity), x is an element of [0, 1] and n the polynomial degree. The shifted Jacobi-Gauss points are used as collocation nodes. Illustrative examples have been discussed to demonstrate the validity and applicability of the proposed technique. Comparing the numerical results of the proposed method with some well-known results show that the method is efficient and gives excellent numerical results.
  • Article
    Citation - WoS: 76
    Citation - Scopus: 82
    On Shifted Jacobi Spectral Approximations for Solving Fractional Differential Equations
    (Elsevier Science inc, 2013) Bhrawy, A. H.; Baleanu, D.; Ezz-Eldien, S. S.; Doha, E. H.
    In this paper, a new formula of Caputo fractional-order derivatives of shifted Jacobi polynomials of any degree in terms of shifted Jacobi polynomials themselves is proved. We discuss a direct solution technique for linear multi-order fractional differential equations (FDEs) subject to nonhomogeneous initial conditions using a shifted Jacobi tau approximation. A quadrature shifted Jacobi tau (Q-SJT) approximation is introduced for the solution of linear multi-order FDEs with variable coefficients. We also propose a shifted Jacobi collocation technique for solving nonlinear multi-order fractional initial value. problems. The advantages of using the proposed techniques are discussed and we compare them with other existing methods. We investigate some illustrative examples of FDEs including linear and nonlinear terms. We demonstrate the high accuracy and the efficiency of the proposed techniques. (C) 2013 Elsevier Inc. All rights reserved.
  • Article
    Citation - WoS: 203
    Citation - Scopus: 217
    A Spectral Tau Algorithm Based on Jacobi Operational Matrix for Numerical Solution of Time Fractional Diffusion-Wave Equations
    (Academic Press inc Elsevier Science, 2015) Doha, E. H.; Baleanu, D.; Ezz-Eldien, S. S.; Bhrawy, A. H.
    In this paper, an efficient and accurate spectral numerical method is presented for solving second-, fourth-order fractional diffusion-wave equations and fractional wave equations with damping. The proposed method is based on Jacobi tau spectral procedure together with the Jacobi operational matrix for fractional integrals, described in the Riemann-Liouville sense. The main characteristic behind this approach is to reduce such problems to those of solving systems of algebraic equations in the unknown expansion coefficients of the sought-for spectral approximations. The validity and effectiveness of the method are demonstrated by solving five 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. (C) 2014 Elsevier Inc. All rights reserved.