I am trying to regenerate the results from "https://www.sciencedirect.com/science/article/abs/pii/S0016003213000276" on non-Newtonian Johnson–Segalman fluid using Adomian Decomposition Method (ADM).

The non-demensionalize form along with the boundary condition were stated in equations 28 and 29.

The coefficients of An's and Bn's were generated in equations 49-56, and I am well agreed with these.

In equation 62 and 63 solution for w1 and w2 were presented, authors calculated these solution using w0 in 47 and recursive relation in 48.

I followed all the steps and tried to get the solution in 62 and 63 stated in the article but didn't get that one presented.

As according to my calculation when one can take derivative of w0 the term 'ln(r)' vanish but how it came in the solution term?

Please guide me where I was doing wrong. I am unable to attach files of my calculation

Looking for guidance.

Thanks