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,...

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Bibliographic Details
Published in:Cybernetics and systems analysis Vol. 56; no. 4; pp. 566 - 576
Main Author: Prikazchikov, V.
Format: Journal Article
Language:English
Published: New York Springer US 01.07.2020
Springer
Springer Nature B.V
Subjects:
Accuracy
Algorithms
Artificial Intelligence
Control
Differential equations
Exact solutions
Linear algebra
Linear equations
Mathematical analysis
Mathematics
Mathematics and Statistics
Matrix methods
Ordinary differential equations
Processor Architectures
Software Engineering/Programming and Operating Systems
Superposition (mathematics)
Systems Theory
system of linear algebraic equations
exact scheme
superposition of solutions
forth-order differential equation
Green function
boundary-value problem
spectral problem
Cauchy problem
Wronskian
scheme of high order of accuracy
linearly independent solutions
grid method
tridiagonal matrix algorithm
functional series
ISSN:1060-0396, 1573-8337
Online Access:Get full text
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Summary: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.
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ISSN:1060-0396
1573-8337
DOI:10.1007/s10559-020-00273-2