Prikazchikov V.
Exact three-point scheme and schemes of high order of accuracy for a forth-order ordinary differential equation

We propose an exact three-point scheme and schemes of high order of accuracy, which are two systems of linear algebraic equations. Each equation of the system contains five unknown values of the exact solution and its first derivative at three grid points on the interval. In constructing the scheme, the principle of superposition of solutions was used. Partial sums of the functional series representing independent solutions provide schemes of arbitrary order of accuracy for the boundary-value poblem and for the spectral one. To solve systems of linear equations, the modified tridiagonal matrix algorithm is proposed. © 2020, Springer Science+Business Media, LLC, part of Springer Nature.

Keywords: boundary-value problem, Cauchy problem, exact scheme, forth-order differential equation, functional series, Green function, grid method, linearly independent solutions, scheme of high order of accuracy, spectral problem, superposition of solutions, system of linear algebraic equations, tridiagonal matrix algorithm, Wronskian, Linear equations, Matrix algebra, Arbitrary order, Boundary values, First derivative, Principle of superposition, Systems of linear algebraic equations, Systems of linear equations, Tri-diagonal matrix algorithms, Unknown values, Ordinary differential equations

Cite:
Prikazchikov V. (2020). Exact three-point scheme and schemes of high order of accuracy for a forth-order ordinary differential equation. Cybernetics and Systems Analysis, 56 (4), 56–67. doi: https://doi.org/10.1007/s10559-020-00273-2 http://jnas.nbuv.gov.ua/article/UJRN-0001129994 [In Russian].