Boundary Value Problems

Table 1 Conformal mappings and nodes for several subintervals of R

From: An efficient computer application of the sinc-Galerkin approximation for nonlinear boundary value problems

(a,b)		ϕ(z)	$z_{k}$
a	b	$ln (\frac{z - a}{b - z})$	$\frac{a + b e^{k h}}{1 + e^{k h}}$
0	1	$ln (\frac{z}{1 - z})$	$\frac{e^{k h}}{1 + e^{k h}}$
0	∞	ln(z)	$e^{k h}$
0	∞	ln(sinh(z))	$ln (e^{k h} + \sqrt{e^{2 k h} + 1})$
−∞	∞	z	kh
−∞	∞	sinh⁻¹(z)	kh

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