Re: Simultaneous difference equation

*To*: mathgroup at smc.vnet.net*Subject*: [mg30607] Re: [mg30600] Simultaneous difference equation*From*: BobHanlon at aol.com*Date*: Fri, 31 Aug 2001 04:09:32 -0400 (EDT)*Sender*: owner-wri-mathgroup at wolfram.com

In a message dated 2001/8/30 4:19:39 AM, shusaku.yamamoto at buseco.monash.edu.au writes: >Hello, I have just started using (or more appropriately trying to use) >Mathematica. As you expect, I have a problem. I would like to know >Mathematica code for solving simultaneous difference eqation; for >example: > >a_11*x(t)+a_12*y(t)=a_13*x(t-1)+a_14*y(t-1)+k_1 >a_21* x(t)+a_22*y(t)=a_23*x(t-1)+a_24*y(t-1)+k_2 > >Or, in matrix notation, > >A_1*Y(t)=A_2*Y(t-1)+K > >t denotes time t, and t-1 is one period before time t. > >I have go through help menu in Mathematica. Yet, I could not get reached >to the topic of difference equation. If you know the code (or what to be >typed), could you reply this message? > There is an entry in the Master Index for difference equations which refers to a standard add-on package. Needs["DiscreteMath`RSolve`"]; Using specific coefficients {{a11, a12, a13, a14}, {a21, a22, a23, a24}} = {{1, 2, 1, 1}, {1, 1, 2, 1}}; and specifying the initial conditions RSolve[ {a11*x[t]+a12*y[t] == a13*x[t-1]+a14*y[t-1]+k1, a21*x[t]+a22*y[t] == a23*x[t-1]+a24*y[t-1]+k2, x[0] == y[0] == 0}, {x[t], y[t]}, t] %//FullSimplify Bob Hanlon Chantilly, VA USA