A note on the existence and uniqueness solutions of the modified error function.

This paper shows that the following nonlinear boundary value problem: ( 1 + δ y ) y ′ ′ + 2 x y ′ = 0 , 0 < x < ∞ , y ( 0 ) = 0 , y ( ∞ ) = 1 , where δ≥ − 1 and y is defined as a modified error function, can be reduced to the boundary value problems for the generalized Emden‐Fowler equation and Abel differential equation of the second kind in the canonical form, which do not usually have closed‐form solutions. The existence and uniqueness of the solution are established by considering another contraction mapping. Highly accurate approximate solutions of this problem are also provided. [ABSTRACT FROM AUTHOR]