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These are questions asked by

fourthNONLINEARBOUD234.mwfourthNONLINEARBOUD234.mw
 

``

NULL

NULL

NULL

[0., 0, 0.]

(1)

restart

with(LinearAlgebra)

``

for i to 1 do for j from 0 by .1 to 1 do Exact[j] := exp(j); Y[0] := proc (x) options operator, arrow; 1+x-(58/9)*x^2-3*x^2*exp(1)+(64/9)*x^2*exp(3/4)+(40/9)*x^3+4*x^3*exp(1)-(64/9)*x^3*exp(3/4) end proc; Ics := Z(0) = 1, (D(Z))(0) = 1, Z(1) = exp(1), Z(3/4) = exp(3/4); exp(-x) := convert(taylor(exp(-x), x = 0, 5), polynom); f := proc (x) options operator, arrow; 0 end proc; p := proc (x) options operator, arrow; 0 end proc; q := proc (x) options operator, arrow; 0 end proc; r := proc (x) options operator, arrow; 0 end proc; u := proc (x) options operator, arrow; 0 end proc; eq[i] := diff(Z(x), `$`(x, 4)) = 0.1e-2*(diff(Y[i-1](x), `$`(x, 4)))+.999*(f(x)+exp(-x)*Y[i-1](x)*Y[i-1](x)); s[i] := dsolve({Ics, eq[i]}, Z(x)); Y[i] := unapply(op(2, s[i]), x); App[j] := evalf(Y[i](j)); Er[j] := abs(App[j]-Exact[j]); A[i] := print([App[j], Exact[j], Er[j]]) end do end do

[1., 1, 0.]

 

[1.105170012, 1.105170918, 0.906e-6]

 

[1.221399998, 1.221402758, 0.2760e-5]

 

[1.349854378, 1.349858808, 0.4430e-5]

 

[1.491819577, 1.491824698, 0.5121e-5]

 

[1.648716753, 1.648721271, 0.4518e-5]

 

[1.822115950, 1.822118800, 0.2850e-5]

 

[2.013751870, 2.013752707, 0.837e-6]

 

[2.225541500, 2.225540928, 0.572e-6]

 

[2.459603808, 2.459603111, 0.697e-6]

 

[2.718281833, 2.718281828, 0.5e-8]

 

[2., 1, 1.]

 

[2., 1.105170918, .894829082]

 

[2., 1.221402758, .778597242]

 

[2., 1.349858808, .650141192]

 

[2., 1.491824698, .508175302]

 

[2., 1.648721271, .351278729]

 

[2., 1.822118800, .177881200]

 

[2., 2.013752707, 0.13752707e-1]

 

[2., 2.225540928, .225540928]

 

[2., 2.459603111, .459603111]

 

[2., 2.718281828, .718281828]

(2)

``

``


 

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