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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
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