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Question: Why doesn't it work correctly?

Question:Why doesn't it work correctly?

hind 45 Maple
recurrence
December 20 2015
0

 

How to  compute the recurrence relation and I find the problem when the summation of U because appear noise term self-canceling and I can not find the nth component of U?Mixed_volterra_-Fredholm_(278)_Ex(8.17).mw

"this program is solving Mixed Fredholmvolterra integral equation using modified decomposition method page 278 Example(8.17) by Creation date : (9\3\1437) ------------------------------ u(x)=f(x,t)+(∫)[0]^(t)(∫)[0]^(1)F(x,t,r,s)*u(r,s) ⅆr ds. -----------------------------"

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restart
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f := proc (x, t) options operator, arrow; exp(-t)*(cos(x)+t*cos(x)+(1/2)*t*cos(x-1)*sin(1)) end proc:
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U[0] := f1(x, t):
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for i from 2 to 5 do U1[i-1] := subs({r = x, s = t}, U[i-1]); U[i] := simplify(-(int(int(F(x, t, r, s)*U1[i-1], r = 0 .. 1), s = 0 .. t))) end do:
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Download Mixed_volterra_-Fredholm_(278)_Ex(8.17).mwMixed_volterra_-Fredholm_(278)_Ex(8.17).mw

 

thank you for helping:)
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