A Numerical Method for Solving Boundary Value Problem for Essentially Loaded Differential Equations

Zh. М. Каdirbayeva

2021

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DOI 10.1134/s1995080221030112
Data confidence 70 medium
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Abstract

Abstract A linear boundary value problem for essentially loaded differential equations is investigated. Using the properties of essentially loaded differential equation and assuming the invertibility of the matrix compiled through the coefficients at the values of the derivative of the desired function at load points, we reduce the considering problem to a two-point boundary value problem for loaded differential equations. The method of parameterization is used for solving the problem. The linear boundary value problem for loaded differential equations by introducing additional parameters at the loading points is reduced to equivalent boundary value problem with parameters. The equivalent boundary value problem with parameters consists of the Cauchy problem for the system of ordinary differential equations with parameters, boundary condition and continuity conditions. The solution of the Cauchy problem for the system of ordinary differential equations with parameters is constructed using the fundamental matrix of differential equation. The system of linear algebraic equations with respect to the parameters are composed by substituting the values of the corresponding points in the built solutions to the boundary condition and the continuity condition. Numerical method for finding solution of the problem is suggested, which based on the solving the constructed system and the Bulirsch–Stoer method for solving Cauchy problem on the subintervals.