@marram When defining phi at the end you make it a function of (n,t,x), but no t appears in the expression. Also in Gterm there appears lambda(j)*t. But what is lambda?

@marram When defining phi at the end you make it a function of (n,t,x), but no t appears in the expression. Also in Gterm there appears lambda(j)*t. But what is lambda?

It works for me in Maple 15 and Maple 16. The elementwise operations of a function f on a container A (list,set Vector, Matrix, Array) works by appending a tilde onto f:   f~(A);

This was introduced in Maple 13.

It works for me in Maple 15 and Maple 16. The elementwise operations of a function f on a container A (list,set Vector, Matrix, Array) works by appending a tilde onto f:   f~(A);

This was introduced in Maple 13.

@marram You write vterm := int(D[2](Gterm)(n,1,x,t-tau),tau=0..t);

but Gterm is a function of 5 variables j,n,x,y,t.

@marram You write vterm := int(D[2](Gterm)(n,1,x,t-tau),tau=0..t);

but Gterm is a function of 5 variables j,n,x,y,t.

@marram I have edited my original answer quite a lot since it was not correct. I looked up the paper you referred to and now know what the authors call the characteristic equation in this context. Sorry about the confusion!

Be aware that in the Maple version they used in 1997 the LinearAlgebra package was not yet introduced. It came with Maple 6. The old package linalg should not be used these days.

@marram I have edited my original answer quite a lot since it was not correct. I looked up the paper you referred to and now know what the authors call the characteristic equation in this context. Sorry about the confusion!

Be aware that in the Maple version they used in 1997 the LinearAlgebra package was not yet introduced. It came with Maple 6. The old package linalg should not be used these days.

@J4James Since Nc appears in the boundary condition at 0 you need to include that in the eval part, like this:

dsolve(eval({eq2,theta(9)=0,D(theta)(0)=-Nc*(1-theta(0))},{beta=1,Ec=0.5,Q=-0.5,Nc=5,pr=3,f(eta)=F(eta),diff(f(eta),eta,eta)=F2(eta)}),numeric,known=[F,F2]):

@J4James Since Nc appears in the boundary condition at 0 you need to include that in the eval part, like this:

dsolve(eval({eq2,theta(9)=0,D(theta)(0)=-Nc*(1-theta(0))},{beta=1,Ec=0.5,Q=-0.5,Nc=5,pr=3,f(eta)=F(eta),diff(f(eta),eta,eta)=F2(eta)}),numeric,known=[F,F2]):

It would be helpful if you gave us the system.

@J4James This is not simple. I tried and have uploaded a worksheet which does get something looking like fig. 2a in the paper. Since infinity = 9 it is not surprising that there is a substantial difference. However, the general shape is good. As could be expected it is tricky at the leftmost end.

MaplePrimes12-09-06B.mw

Although you don't give me all the necessary details, the loop is not OK:

A := []; for e from -1 by .1 to 3 do solk := dsolve({icsys, op(subs(k = 10^e, sysk))}, numeric,

 known = [A, A1, A2, A3]); deltk := subs(solk, Delta[d](t)); 

A := [op(A), [e, log10(deltk(.9)^2)]] end do;

A is defined to be a list initially, thus not the name of a procedure. That alone would cause an error.
Secondly A is again defined to be a list at the end of the loop and furthermore

[e, log10(deltk(.9)^2)] is again a list, and not even of names of procedures.

Although you don't give me all the necessary details, the loop is not OK:

A := []; for e from -1 by .1 to 3 do solk := dsolve({icsys, op(subs(k = 10^e, sysk))}, numeric,

 known = [A, A1, A2, A3]); deltk := subs(solk, Delta[d](t)); 

A := [op(A), [e, log10(deltk(.9)^2)]] end do;

A is defined to be a list initially, thus not the name of a procedure. That alone would cause an error.
Secondly A is again defined to be a list at the end of the loop and furthermore

[e, log10(deltk(.9)^2)] is again a list, and not even of names of procedures.

@J4James Is Lambda (or Omega) given in advance and the parameters s and lambda to be determined? Or is s also given and only lambda to be determined?