Union of Piecewise Functions

*To*: mathgroup at smc.vnet.net*Subject*: [mg55695] Union of Piecewise Functions*From*: Pratik Desai <pdesai1 at umbc.edu>*Date*: Sun, 3 Apr 2005 05:51:05 -0400 (EDT)*Sender*: owner-wri-mathgroup at wolfram.com

Hello All, I am trying to compute a series solution for a PDE with a jump discontinuity in the domain (Wave equation for a string with a damper collocated inside the domain 0<x<l). Briefly, I am trying to accomplish these tasks: I have series solution for the part 0<x<d resp1[x_,t_,n_]:=Total[(1/sec3[n])*phig[x,n]*An1[t,n]]+Total[(1/Conjugate[sec3[n]])*phigc[x,n]*An2[t,n]]//Chop where An1[t] is obtained by solving a first order ode in terms of time expr1=an'[t]-lamda*an[t]; sol1=DSolve[expr1==UnitStep[t],an,t]/.{C[1]->0}; phig1[x,n] is my spatial eigenfunction say Sin[n*pi*x/L] sec3[n] is some scaling (fouirer) coefficient (not a function of x, ignorable for the present purpose ) Similarly for d<x<l resp2[y_,t_,n_]:=Total[(1/sec4[n])*phig[(l-x),n]*An1[t,n]]+Total[(1/Conjugate[sec4[n]])*phigc[(l-x),n]*An2[t,n]]//Chop At d respd[d_,t_,n_]=Total[(1/sec3[n])*y[d]*An1[t,n]]+Total[(1/Conjugate[sec3[n]])*y[d]*An2[t,n]]//Chop Now I am trying to find the complete response by using Union, resp[x_,y_,t_,n_]:=Union[resp1[(x-d),t,n],respd[d,t,n],resp2[y,t,n]] (*not sure about this*) d=0.4 (*assume*) m=3 Table[resp[x,y,t,n],{x,0,0.7,0.1},{y,0.7,1,0.1},{t,0,10,1},{n,1,m,1}] is there a better way to accomplish this, any ideas will be greatly appreciated. I would like to plot these for different values of t to check for convergence. Thanks again, Best Regards, Pratik Desai