sorry, the initial and boundary conditions should have been IBC := n(x,0)=piecewise(x^2<1,0,x^2>1,1),m(x,0)=piecewise(x^2>1,0,x^2<1,1),C[1](x,0)=1,C[1](infinity,t)=1,n(infinity,t)=1,m(infinity,t)=0,n(-infinity,t)=1,m(-infinity,t)=0,C[1](-infinity,0)=1; and I have defined the known functions and values as follows: a[i]:=i/(2*i):h[i]:=i/i:b[i]:=i/i: d:=0.01:d[1]:=1:N:=100:P[1]:=0:H:=1: r:=y->(N-y)/(N-1); s[1]:=y->a[i]+(1-a[i])*y; p[1]:=y->h[i](1+b[i])/(1+b[i]*y^2);