  Blasius boundary layer solution is a Maclaurin series expansion of the
function \(f(\eta)\), which has convergence problems when evaluating for higher
values of \(\eta\) due to a singularity present at \(\eta\approx-5.69\). In
this paper we are introducing an accurate solution to \(f(\eta)\) using
Taylor's series expansions with progressively shifted centers of
expansion(Leaping centers). Each series is solved as an IVP with the three
initial values computed from solution of the previous series, so the gap
between the centers of two consecutive expansions is selected from within the
convergence disc of the first series. The last series is formed such that it is
convergent for a reasonable high \(\eta\) value needed for implementing the
boundary condition at infinity. The present methodology uses Newton-Raphson
method to compute the value of the unknown initial condition viz. \(f''(0)\) in
an iterative manner. Benchmark accurate results of different parameters of flat
plate boundary layer with no slip and slip boundary conditions have been
reported in this paper.
