Mohamed ELARBİ BENATTİA, Kacem BELGHABA, Bouteraa NOUREDDİNE

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

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.

Keywords:

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

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[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.