UDC 519.6
EXACT THREE-POINT SCHEME AND SCHEMES OF HIGH ORDER OF ACCURACY
FOR A FORTH-ORDER ORDINARY DIFFERENTIAL EQUATION
Abstract. We propose a 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 give schemes of arbitrary order of accuracy for the boundary problem and for the spectral one. To solve systems of linear equations,
the modified ribbon matrix algorithm is proposed.
Keywords: forth-order differential equation, boundary-value problem, spectral problem, initial value problem, linearly independent solutions,
Wronskian, superposition of solutions, Green function, grid method, exact scheme, scheme of high order of accuracy, functional series,
system of linear algebraic equations, ribbon matrix algorithm.
FULL TEXT
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