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Mann iterative method...

Asked: 10 Product: Maple 2021

February 15 2022

1 2

PDETWOSTEPVARIAMETHOD.mwPDETWOSTEPVARIAMETHOD.mw

Pls i need help to correct this iteration code, I wrote but is not given the correct answer. find attached the worksheet

Boundary Value Problem, some iteration w...

Asked: 10 Product: Maple 14

April 29 2021

0 0

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$for i to 7 do for j from -1 by .1 to 1 do Exact[j] := ((1-j)*(1/2))*exp((1+j)*(1/2)); Y[0] := proc (x) options operator, arrow; -(1/8)*exp(1)+1/2+(-(1/8)*exp(1)-3/4)*x+(1/8)*exp(1)*x^2+((1/8)*exp(1)+1/4)*x^3 end proc; Ics := Z(-1) = 1, Z(1) = 0, (D(Z))(-1) = 0, (D(Z))(1) = -(1/2)*exp(1); exp(x) := convert(taylor(exp(x), x = 0, 25), polynom); f := proc (x) options operator, arrow; ((1/32)*x-5/32)*exp((1/2)*x+1/2) end proc; p := proc (x) options operator, arrow; 0 end proc; q := proc (x) options operator, arrow; -1/4 end proc; r := proc (x) options operator, arrow; 0 end proc; u := proc (x) options operator, arrow; -1/16 end proc; eq[i] := diff(Z(x), `$`(x, 4)) = (1-alpha)*(diff(Y[i-1](x), `$`(x, 4)))+alpha*(f(x)-p(x)*(diff(Y[i-1](x), `$`(x, 3)))-q(x)*(diff(Y[i-1](x), `$`(x, 2)))-r(x)*(diff(Y[i-1](x), x))-u(x)*Y[i-1](x)); s[i] := evalf(dsolve({Ics, eq[i]}, Z(x))); Y[i] := unapply(op(2, s[i]), x); App[j] := evalf(Y[i](j)); Er[j] := abs(App[j]-Exact[j]); print([App[j], Exact[j], Er[j]]) end do end do$

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Download fourthLINEARBOUD042021.mw

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Download fourthLINEARBOUD042021.mw

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Download fourthLINEARBOUD042021.mw

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Download fourthLINEARBOUD042021.mw

PLS FIND ATTACHED A MAPLE CODE TO SOLVE SOME BOUNDARY VALUE PROBLEM, BUT IT JUMP SOME ITERATION WITHOUT EVALUATION WHICH END UP WITH INACCURATE SOLUTION.

> restart;
> with(LinearAlgebra);
> exp(1) := 2.7182818284590452354;
> alpha := .975;
> NULL;
> st := time[real]();
> for i to 4 do for j from 0 by .1 to 4-exp(1) do Exact[j] := evalf(ln(exp(1)+j)); Y[0] := proc (x) options operator, arrow; 1+x/exp(1)+(1/4)*((exp(1))^2-8*exp(1)+24*ln(2)*exp(1)-32)*x^2/(exp(1)*(16-8*exp(1)+(exp(1))^2))+(1/4)*(16*ln(2)*exp(1)-16-8*exp(1)+(exp(1))^2)*x^3/((-64+48*exp(1)-12*(exp(1))^2+(exp(1))^3)*exp(1)) end proc; Ics := Z(0) = 1, (D(Z))(0) = 1/exp(1), Z(4-exp(1)) = evalf(ln(4)), (D(Z))(4-exp(1)) = 1/4; 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), `$`(x, 4)) = (1-alpha)*(diff(Y[i-1](x), `$`(x, 4)))+alpha*(-6*convert(taylor(exp(-4*Y[i-1](x)), x = 0, 20), polynom)); 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]); print([App[j], Exact[j], Er[j]]) end do end do; time[real]()-st;

`Please HOW CAN USE MAPLE IN SOLVI...

Asked: 10 Product: Maple 2019

October 10 2019

1 0

fourthNONLINEARBOUD234.mwfourthNONLINEARBOUD234.mw

NULL

(1)

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