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 Mat. Zametki: Year: Volume: Issue: Page: Find

 Mat. Zametki, 2012, Volume 91, Issue 6, Pages 803–812 (Mi mz8958)

On a Numerical Method for Constructing a Positive Solution of the Two-Point Boundary-Value Problem for a Second-Order Nonlinear Differential Equation

E. I. Abduragimov

Daghestan Scientific Centre of the Russian Academy of Sciences

Abstract: An iterative method is proposed for finding an approximation to the positive solution of the two-point boundary-value problem
$$y"+c(x)y^m=0,\quad 0<x<1,\qquad y(0)=y(1)=0,$$
where $m=\mathrm{const}>1$ and $c(x)$ is a continuous nonnegative function on $[0,1]$. The convergence of this method is proved. An error estimate is also obtained.

Keywords: second-order nonlinear differential equation, two-point boundary-value problem, elliptic differential equation, Cauchy problem, Green function

DOI: https://doi.org/10.4213/mzm8958

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English version:
Mathematical Notes, 2012, 91:6, 755–763

Bibliographic databases:

Document Type: Article
UDC: 519.62

Citation: E. I. Abduragimov, “On a Numerical Method for Constructing a Positive Solution of the Two-Point Boundary-Value Problem for a Second-Order Nonlinear Differential Equation”, Mat. Zametki, 91:6 (2012), 803–812; Math. Notes, 91:6 (2012), 755–763

Citation in format AMSBIB
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