摘要：In this paper, we present a numerical functional anathe one-of the mixed Schauder basis and the leastIntroducMtioonst of linear differential or diffspaceof the following second order hyperbolic problem:2 22 2 u ut u u F(x,t), x t t x with initial conditionsu(x,0) f(x), 0 x 1,( ,0) ( ), 0 1, t u x g x x and boundary conditionsu(0,t) p(t), 0 t u(1,t) q(t), 0 t ,Where , are know constant coefficients andF : L2[0,1][0,] are known function, while the functions, while theunknown.Equation (1), is referred to as the seconddiffusion and wave propagation by introducing a term that accounts(El-Azab and El-Gamel, 2007; Dehghan and Spropagation of electrical signals (Metaxas and R.J. Meredith, 1993;other fields (see Roussy and Pearcy, 1995suitable than ordinary diffusion equation in modeling the reaction diDehghan, 2008).With twice integrating Eq. (1) on (0,t), , analysis least-thfferential-byperbolic 0 1, 0 ,,f,g : L2[0,1] and L [Lhe second-order telegraph equation with constant coeffusion finnite Shokri, 2008). trans1995and the references usion diffusion ,that 0 < t < and using Eqs. (2) andS (1), J20C1R6S: 33-40boundary control of aTelegraph equation, Hyperbolic equation, Best approximation, Sobolev space, Least-squareslysis method for approximations the solution ofdimensional hyperbolic telegraph equation. We formulate a general problem in a Sobolev space making usesquares method to approximate the load function and the solution of thegeneral problem. In addition, we give a convergence result and a numerical solution of the telegraph problem
关键词：.;ABSTRACT: In this paper; we present a numerical functional ana;the one-of the mixed Schauder basis and the least;IntroducMtioonst of linear differential or diff;space;of the following second order hyperbolic problem:;2 2;2 2 u ut u u F(x;t); x t t x with initial conditions;u(x;0) f(x); 0 x 1;( ;0) ( ); 0 1; t u x g x x ;and boundary conditions;u(0;t) p(t); 0 t ;u(1;t) q(t); 0 t ;Where ; are know constant coefficients and;F : L2[0;1][0;] are known function; while the functions; while the;unknown.;Equation (1); is referred to as the second;diffusion and wave propagation by introducing a term that accounts;(El-Azab and El-Gamel; 2007; Dehghan and S;propagation of electrical signals (Metaxas and R.J. Meredith; 1993;other fields (see Roussy and Pearcy; 1995;suitable than ordinary diffusion equation in modeling the reaction di;Dehghan; 2008).;With twice integrating Eq. (1) on (0;t); ; analysis least-th;fferential-b;yperbolic 0 1; 0 ;f;g : L2[0;1] and L [;L;he second-order telegraph equation with constant coeff;usion finnite Shokri; 2008). trans;1995;and the references usion diffusion ;that 0 < t < and using Eqs. (2) and;S (1); J20C1R6S: 33-40;boundary control of a;Telegraph
