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(*DefinethefunctionT(x)basedonthegivenT(x)inExample4*)T[x_]:=(3/4)*(x+1/x)(*Definetheparameters*)m=1;a0=1;iterations=5;(*Initializeliststostoreiterationvalues*)a={N[a0]};b={};c={};(*Definetheimplicitequationforc_n*)implicitEquation[a_,c_]:=c==(m/(m+1))*a+(1/(m+1))*T[c]n=1;converged=True;While[n<=iterations&&converged,(*Solveforc_nimplicitly*)Print["Iteration: ",n];Print["Current a[[n]]: ",a[[n]]];c_n=Quiet[FindRoot[implicitEquation[a[[n]],c],{c,a[[n]]}]];If[NumericQ[c_n[[1,2]]],(*Appendthefoundc_ntothelist*)c=Append[c,N[c_n[[1,2]]]];(*Calculateb_n*)b_n=T[c[[-1]]];b=Append[b,N[b_n]];(*Calculatea_(n+1)*)a_n1=T[b_n];a=Append[a,N[a_n1]];Print["Computed c_n: ",c[[-1]]];Print["Computed b_n: ",b_n];Print["Computed a_(n+1): ",a_n1];,(*Handlenon-numericc_n*)converged=False;MessageDialog["Error: Non-numeric value encountered in iteration "<>ToString[n]];];n++;](*Displaytheresultsinatable*)TableForm[Transpose[{Range[0,Length[a]-1],a}],TableHeadings->{None,{"Iteration","a"}}](*Plottheresults*)ListLinePlot[a,PlotMarkers->Automatic,GridLines->Automatic,AxesLabel->{"Iteration","a"},PlotLabel->"Implicit Iterations of Example 4"]
Iteration: 1
Current a[[n]]: 1.
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Iteration | a |
0 | 1. |
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