boundary value problem
for a third order differential equation
with variable coefficients is
considered. The questions of the existence of a unique solution of the considered problem and ways of its construction are investigated. The multipoint-integral boundary value problem for the differential equation of third order
with variable coefficients is reduced to a multipoint-integral boundary value problem for a system of three differential equations by introducing new functions. To solve the resulting multipoint-integral boundary value problem, a parametrization method
is applied. Algorithms
of finding the approximate solution
to the multipoint-integral boundary value problem for the system of three differential equations are constructed and their convergence is proved. The conditions of the unique solvability
of the multipoint-integral boundary value problem for the system of three differential equations are established in the terms of initial data. The results are also formulated relative to the original of the multipoint-integral boundary value problem for the differential equation of third order
with variable coefficients. The obtained results are applied to a two-point boundary value problem for the third order ordinary differential equation.
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Über dieses Kapitel
Solvability of Multipoint-Integral Boundary Value Problem for a Third-Order Differential Equation and Parametrization Method