The Kidder problem is uxx+2x(1-αu)-1/2ux=0 with u(0)=1 and u(∞)=0 where α∈[0,1]. This looks challenging because of the square root singularity. We prove, however, that |u(x;α)-erfc(x)|≤0.046 for all x,α. Other very simple but very accurate curve fits and bounds are given in the text; |u(x;α)-erfc(x+0.15076x/(1+1.55607x2))|≤0.0019. Maple code for a rational Chebyshev pseudospectral method is given as a table. Convergence is geometric until the coefficients are O(10-12) when the coefficients an∼constant/n-6. An initial-value problem is obtained if ux(0,α) is known; the slope Chebyshev series has only a fourth-order rate of convergence until a simple change-of-coordinate restores a geometric rate of convergence, empirically proportional to exp(-n/8). Kidder's perturbation theory (in powers of α) is much inferior to a delta-expansion given here for the first time. A quadratic-over-quadratic Padé approximant in the exponentially mapped coordinate z=erf(z) predicts the slope at the origin very accurately up to about α≈0.8. Finally, it is shown that the singular case u(x;α=1) can be expressed in terms of the solution to the Blasius equation. © 2014 Wiley Periodicals, Inc.

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