Taylor polynomial solution of hyperbolic type partial differential equations with constant coefficients

Abstract

The purpose of this study is to give a Taylor polynomial approximation for the solution of hyperbolic type partial differential equations with constant coefficients. The technique used is an improved Taylor matrix method, which has been given for solving ordinary differential, integral and integro-differential equations [M. Gulsu and M. Sezer, A method for the approximate solution of the high-order linear difference equations in terms of Taylor polynomials, Int. J. Comput. Math. 82(5) (2005), pp. 629-642; M. Gulsu and M. Sezer, On the solution of the Riccati equation by the Taylor matrix method, Appl. Math. Comput. 188 (2007), pp. 446-449; A. Karamete and M. Sezer, A Taylor collocation method for the solution of linear integro-differential equations, Int. J. Comput. Math. 79(9) (2002), pp. 987-1000; N. Kurt and M. Cevik, Polynomial solution of the single degree of freedom system by Taylor matrix method, Mech. Res. Commun. 35 (2008), pp. 530-536; N. Kurt and M. Sezer, Polynomial solution of high-order linear Fredholm integro-differential equations with constant coefficients, J. Franklin Inst. 345 (2008), pp. 839-850; , S. Nas, S. Yalcinbas, and M. Sezer, A method for approximate solution of the high-order linear Fredholm integro-differential equations, Int. J. Math. Edu. Sci. Technol. 27(6) (1996), pp. 821-834; M. Sezer, Taylor polynomial solution of Volterra integral equations, Int. J. Math. Edu. Sci. Technol. 25(5) (1994), pp. 625-633; M. Sezer, A method for approximate solution of the second order linear differential equations in terms of Taylor polynomials, Int. J. Math. Edu. Sci. Technol. 27(6) (1996), pp. 821-834; M. Sezer, M. Gulsu, and B. Tanay, A matrix method for solving high-order linear difference equations with mixed argument using hybrid Legendre and Taylor polynomials, J. Franklin Inst. 343 (2006), pp. 647-659; S. Yalcinbas, Taylor polynomial solutions of nonlinear Volterra-Fredholm integral equation, Appl. Math. Comput. 127 (2002), pp. 196-206; S. Yalcinbas and M. Sezer, The approximate solution of high-order linear Volterra-Fredholm integro-differential equations in terms of Taylor polynomials, Appl. Math. Comput. 112 (2000), pp. 291308]. Some numerical examples, which consist of initial and boundary conditions, are given to illustrate the reliability and efficiency of the method. Also, the results obtained are compared by the known results; the error analysis is performed and the accuracy of the solution is shown.