Clear[]

F= NDSolve[{(x-2)*y''[x] +y'[x]+(x-2)*Tan[x]*y[x]==0,y[3]==1, y'[3]==2},y,{x,3,13}]//Quiet

DSolve

TruePlot = Plot[Evaluate[y[x]/.F],{x,3,4}, PlotStyle->{Red,Thickness[0.001]}]

This was with h=0.01, points = 201

ODEData6 = Import["C:\\Users\\kfrin\\Desktop\\MPI\\ODEsoln6.dat"];

APDataPlot6 = ListPlot[ODEData6, PlotStyle->Blue];

Show[TruePlot, APDataPlot6]

ODES[x_]:=Evaluate[y[x]/.F][[1]]

ODES[1]

Length[ODEData6]

DiffData = Table[{ODEData6[[i,1]],Abs[(ODES[ODEData6[[i,1]]]-ODEData6[[i,2]])/1.0]},{i,1,Length[ODEData6]}];

ListPlot[DiffData, PlotRange->All]

DiffData2 = Table[{ODEData6[[i,1]],Abs[(ODES[ODEData6[[i,1]]]-ODEData6[[i,2]])/(ODES[ODEData6[[i,1]]])]},{i,1,Length[ODEData6]}];

Plot6 = ListPlot[DiffData2, PlotRange->All];

ODEData6a = Import["C:\\Users\\kfrin\\Desktop\\MPI\\ODEsoln6a.dat"];

APDataPlot6a = ListPlot[ODEData6a, PlotStyle->Blue];

Show[TruePlot, APDataPlot6a]

DiffData2a = Table[{ODEData6a[[i,1]],Abs[(ODES[ODEData6a[[i,1]]]-ODEData6a[[i,2]])/(ODES[ODEData6a[[i,1]]])]},{i,1,Length[ODEData6a]}];

Plot6a = ListPlot[DiffData2a, PlotRange->All, PlotStyle->{Red, PointSize[0.001]}];

Show[Plot6,Plot6a]