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Bilateral method of solution of the linear one-dimensional boundary value problems for second order equations. (Ukrainian) Zbl 0924.34020
Using the Green function $$G(x,s)$$ of the problem $y''(x)=\lambda\rho(x)y+f(x), {MBW(y)}=\omega,$ the authors reduce this problem to the integral equation $$y(x)=g(x)+\lambda\int_{a}^{b} K(x,s)y(s)ds$$, with $g(x)=r(x)+\int_{a}^{b}G(x,s)f(s)ds, \quad K(x,s)=G(x,s)\rho(s),$ and the function $$r(x)$$ is a solution to the problem $$r''(x)=0, MBW(r)=\omega$$. Then, the authors propose an algorithm to construct a bilateral approximation of a solution to the integral equation. Conditions of validity of this method are given.
##### MSC:
 34B27 Green’s functions for ordinary differential equations