00.511.522.533.5400.511.522-D Stagnation Point Similarity Solutionetaf'', f', and fZn2,Zn3,Zn4,Zn1,n1 num_steps..:=Now generate a plot of the similarity variables:Note that I have iterated with various guesses until the correct Y1guess value was found (close enough).Znum_steps 1+3,1.00000403=Check the value of Y2 at "infinity" to see if it is equal to 1:ZRkadapt YBCηstart,ηend,num_steps,D,():=num_steps2000:=ηend10:=ηstart0:=Here the function Rkadapt is used, which is similar to rkfixed except it internally uses adaptable spacing instead of fixed spacing (more accuracy where needed). It reports at fixed spacing however.Now calculate the solution as ηmarches from ηstart to ηend. Here Z is the solution matrix, where the first column is η, the second column is Y1, the third column is Y2, and the fourth column is Y3.YBC1.232587700⎛⎜⎜⎝⎞⎟⎟⎠=YBCY1guessY2BCY3BC⎛⎜⎜⎝⎞⎟⎟⎠:=Set up a vector of the boundary conditions for vector Y at η= 0 and verify:Y3BC0:=Y2BC0:=Y1guess1.2325877:=Define the boundary conditions at η= 0. Note that Y1at η= 0 must be guessed since it is not known.
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