Araştırma Makalesi
BibTex RIS Kaynak Göster

Yıl 2018, Cilt: 1 Sayı: 1, 69 - 76, 30.06.2018

Mohamed Elarbi Benattia , Kacem Belghaba Bouteraa Noureddine

https://doi.org/10.33401/fujma.416273

Öz

Kaynakça

  • [1] M. ELARBI BENATTIA, K. BELGHABA. Application of the Galerkin Method with ChebyshevPolynomials for Solving the Integral Equation.Journal of Computer Science & ComputationalMathematics, DOI: 10.20967/jcscm.2017.03.008.
  • [2] M. ELARBI BENATTIA, K. BELGHABA. Numerical Solution for Solving Fractional DifferentialEquations using Shifted Chebyshev Wavelet. General Letters in Mathematics Vol. 3, No.2, Oct 2017, pp.101-110.
  • [3] Mohamed A. Ramadana, Kamal R. Raslanb, Talaat S. El Danafa, Mohamed A. Abd El Salamb.Solving systems of high-order ordinary differential equations with variable coefficients by exponentialChebyshev collocation method. Journal of Modern Methods in Numerical Mathematics8:1-2 (2017), 40–51.
  • [4] Mehdi Dehghan, Mohammad Shakourifar, and Asgar Hamidi, The solution of linear and nonlinearsystems of volterra functional equations using adomian–pade technique, Chaos, Solutions& Fractals 39 (2009), no. 5, 2509–2521.
  • [5] Elcin Gokmen and Mehmet Sezer, Taylor collocation method for systems of high-order lineardifferential–difference equations with variable coefficients, Ain Shams Engineering Journal 4(2013), no. 1, 117–125.
  • [6] F. Baharifard . Saeed Kazem . K. Parand. Rational and Exponential Legendre Tau Methodon Steady Flow of a Third Grade Fluid in a Porous Half Space, Int. J. Appl. Comput. Math(2016) 2:679–698.
  • [7] Hossein Jafari and Varsha Daftardar-Gejji, Revised adomian decomposition method for solvingsystems of ordinary and fractional differential equations, Applied Mathematics and Computation181 (2006), no. 1, 598–608.
  • [8] IH Abdel-Halim Hassan, Application to differential transformation method for solving systemsof differential equations, Applied Mathematical Modeling 32 (2008), no. 12, 2552–2559.
  • [9] Nebiye Korkmaz and Mehmet Sezer, An approach to numerical solutions of system of high-orderlinear differential-difference equations with variable coefficients and error estimation based onresidual function, New Trends in Mathematical Sciences 2 (2014), no. 3, 220–233.
  • [10] Mehdi Tatari and Mehdi Dehghan, Improvement of hes variational iteration method for solvingsystems of differential equations, Computers & Mathematics with Applications 58 (2009), no.11, 2160–2166.
  • [11] Montri Thongmoon and Sasitorn Pusjuso, The numerical solutions of differential transformmethod and the Laplace transform method for a system of differential equations, NonlinearAnalysis: Hybrid Systems 4 (2010), 425–431.
  • [12] Salih Yalçınbas, Nesrin Özsoy, and Mehmet Sezer, Approximate solution of higher order lineardierential equations by means of a new rational chebyshev collocation method, Mathematical& Computational Applications 15 (2010), no. 1, 45–56.

A comparison study for solving systems of high-order ordinary differential equations with constants coefficients by exponential Legendre collocation method

Yıl 2018, Cilt: 1 Sayı: 1, 69 - 76, 30.06.2018

Mohamed Elarbi Benattia , Kacem Belghaba Bouteraa Noureddine

https://doi.org/10.33401/fujma.416273

Öz

In this article we are interested to study the use of the Legendre exponential (EL) collocation method to solve systems of high order linear ordinary differential equations with constant coefficients. The method transforms the system of differential equations and the conditions given by matrix equations with constant coefficients a new system of equations that corresponds to the system of linear algebraic equations which can be solved . Numerical problems are given to illustrate the validity and applicability of the method. For obtaining the approximate solution Maple software is used.

Anahtar Kelimeler

Exponential Legendre functions System of ordinary differential equations Collocation method System of linear algebraic equations

Kaynakça

  • [1] M. ELARBI BENATTIA, K. BELGHABA. Application of the Galerkin Method with ChebyshevPolynomials for Solving the Integral Equation.Journal of Computer Science & ComputationalMathematics, DOI: 10.20967/jcscm.2017.03.008.
  • [2] M. ELARBI BENATTIA, K. BELGHABA. Numerical Solution for Solving Fractional DifferentialEquations using Shifted Chebyshev Wavelet. General Letters in Mathematics Vol. 3, No.2, Oct 2017, pp.101-110.
  • [3] Mohamed A. Ramadana, Kamal R. Raslanb, Talaat S. El Danafa, Mohamed A. Abd El Salamb.Solving systems of high-order ordinary differential equations with variable coefficients by exponentialChebyshev collocation method. Journal of Modern Methods in Numerical Mathematics8:1-2 (2017), 40–51.
  • [4] Mehdi Dehghan, Mohammad Shakourifar, and Asgar Hamidi, The solution of linear and nonlinearsystems of volterra functional equations using adomian–pade technique, Chaos, Solutions& Fractals 39 (2009), no. 5, 2509–2521.
  • [5] Elcin Gokmen and Mehmet Sezer, Taylor collocation method for systems of high-order lineardifferential–difference equations with variable coefficients, Ain Shams Engineering Journal 4(2013), no. 1, 117–125.
  • [6] F. Baharifard . Saeed Kazem . K. Parand. Rational and Exponential Legendre Tau Methodon Steady Flow of a Third Grade Fluid in a Porous Half Space, Int. J. Appl. Comput. Math(2016) 2:679–698.
  • [7] Hossein Jafari and Varsha Daftardar-Gejji, Revised adomian decomposition method for solvingsystems of ordinary and fractional differential equations, Applied Mathematics and Computation181 (2006), no. 1, 598–608.
  • [8] IH Abdel-Halim Hassan, Application to differential transformation method for solving systemsof differential equations, Applied Mathematical Modeling 32 (2008), no. 12, 2552–2559.
  • [9] Nebiye Korkmaz and Mehmet Sezer, An approach to numerical solutions of system of high-orderlinear differential-difference equations with variable coefficients and error estimation based onresidual function, New Trends in Mathematical Sciences 2 (2014), no. 3, 220–233.
  • [10] Mehdi Tatari and Mehdi Dehghan, Improvement of hes variational iteration method for solvingsystems of differential equations, Computers & Mathematics with Applications 58 (2009), no.11, 2160–2166.
  • [11] Montri Thongmoon and Sasitorn Pusjuso, The numerical solutions of differential transformmethod and the Laplace transform method for a system of differential equations, NonlinearAnalysis: Hybrid Systems 4 (2010), 425–431.
  • [12] Salih Yalçınbas, Nesrin Özsoy, and Mehmet Sezer, Approximate solution of higher order lineardierential equations by means of a new rational chebyshev collocation method, Mathematical& Computational Applications 15 (2010), no. 1, 45–56.
Toplam 12 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Matematik
Bölüm Makaleler
Yazarlar

Mohamed Elarbi Benattia

Kacem Belghaba

Bouteraa Noureddine

Yayımlanma Tarihi 30 Haziran 2018
Gönderilme Tarihi 17 Nisan 2018
Kabul Tarihi 5 Haziran 2018
Yayımlandığı Sayı Yıl 2018 Cilt: 1 Sayı: 1

Kaynak Göster

APA Elarbi Benattia, M., Belghaba, K., & Noureddine, B. (2018). A comparison study for solving systems of high-order ordinary differential equations with constants coefficients by exponential Legendre collocation method. Fundamental Journal of Mathematics and Applications, 1(1), 69-76. https://doi.org/10.33401/fujma.416273
AMA Elarbi Benattia M, Belghaba K, Noureddine B. A comparison study for solving systems of high-order ordinary differential equations with constants coefficients by exponential Legendre collocation method. Fundam. J. Math. Appl. Haziran 2018;1(1):69-76. doi:10.33401/fujma.416273
Chicago Elarbi Benattia, Mohamed, Kacem Belghaba, ve Bouteraa Noureddine. “A Comparison Study for Solving Systems of High-Order Ordinary Differential Equations With Constants Coefficients by Exponential Legendre Collocation Method”. Fundamental Journal of Mathematics and Applications 1, sy. 1 (Haziran 2018): 69-76. https://doi.org/10.33401/fujma.416273.
EndNote Elarbi Benattia M, Belghaba K, Noureddine B (01 Haziran 2018) A comparison study for solving systems of high-order ordinary differential equations with constants coefficients by exponential Legendre collocation method. Fundamental Journal of Mathematics and Applications 1 1 69–76.
IEEE M. Elarbi Benattia, K. Belghaba, ve B. Noureddine, “A comparison study for solving systems of high-order ordinary differential equations with constants coefficients by exponential Legendre collocation method”, Fundam. J. Math. Appl., c. 1, sy. 1, ss. 69–76, 2018, doi: 10.33401/fujma.416273.
ISNAD Elarbi Benattia, Mohamed vd. “A Comparison Study for Solving Systems of High-Order Ordinary Differential Equations With Constants Coefficients by Exponential Legendre Collocation Method”. Fundamental Journal of Mathematics and Applications 1/1 (Haziran 2018), 69-76. https://doi.org/10.33401/fujma.416273.
JAMA Elarbi Benattia M, Belghaba K, Noureddine B. A comparison study for solving systems of high-order ordinary differential equations with constants coefficients by exponential Legendre collocation method. Fundam. J. Math. Appl. 2018;1:69–76.
MLA Elarbi Benattia, Mohamed vd. “A Comparison Study for Solving Systems of High-Order Ordinary Differential Equations With Constants Coefficients by Exponential Legendre Collocation Method”. Fundamental Journal of Mathematics and Applications, c. 1, sy. 1, 2018, ss. 69-76, doi:10.33401/fujma.416273.
Vancouver Elarbi Benattia M, Belghaba K, Noureddine B. A comparison study for solving systems of high-order ordinary differential equations with constants coefficients by exponential Legendre collocation method. Fundam. J. Math. Appl. 2018;1(1):69-76.
 Kapak Resmi İndir

Creative Commons License
The published articles in Fundamental Journal of Mathematics and Applications are licensed under a