Analytical solution to the nonlinear singular boundary value problem arising in biology. (English) Zbl 1383.34041
From the summary and introduction: Consider the two-point boundary value problem of the type
\[
\begin{gathered} y''(x)+ ny'(x)+{m\over x} y'(x)= f(x,y(x)),\quad 0< x\leq 1,\;m>0,\;n\in\mathbb{R},\\ y'(0)= 0,\quad Ay(1)+ By'(1)= C.\end{gathered}
\]
As a first step, we present a constructive proof of the existence and uniqueness of solution. Then, we apply the Picard iterative sequence by constructing an integral equation whose Green’s function is not negative. The convergence of this iterative sequence is then controlled by an embedded parameter so that it tends to the unique solution.
MSC:
| 34B16 | Singular nonlinear boundary value problems for ordinary differential equations |
| 34A45 | Theoretical approximation of solutions to ordinary differential equations |
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