Three-Point Difference Schemes of High Order of Accuracy for the Sturm–Liouville Problem

For the Sturm–Liouville problem, we construct three-point difference schemes of high order of accuracy on a nonuniform grid. The proposed difference schemes for each node of the grid x j , j = 1,2,…, N − 1, require solving of two Cauchy problems for the second-order linear ordinary differential equa...

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Veröffentlicht in:Journal of mathematical sciences (New York, N.Y.) Jg. 273; H. 6; S. 948 - 959
Hauptverfasser: Kunynets, A. V., Kutniv, M. V., Khomenko, N. V.
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Cham Springer International Publishing 04.07.2023
Springer
Springer Nature B.V
Schlagworte:
Accuracy
Algorithms
Basketball players
Cauchy problems
Differential equations
Eigenvalues
Mathematics
Mathematics and Statistics
Ordinary differential equations
Runge-Kutta method
Series expansion
Sturm-Liouville theory
Taylor series
three-point difference scheme of any order of accuracy
Sturm–Liouville problem
exact three-point difference scheme
Newton’s iterative method
ISSN:1072-3374, 1573-8795
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Zusammenfassung:For the Sturm–Liouville problem, we construct three-point difference schemes of high order of accuracy on a nonuniform grid. The proposed difference schemes for each node of the grid x j , j = 1,2,…, N − 1, require solving of two Cauchy problems for the second-order linear ordinary differential equations on the segments [ x j −1 , x j ] (forward) and [ x j , x j +1 ] (backward) carried out for a single step by using an arbitrary one-step method: either the Taylor series expansion or the Runge–Kutta method of the order of accuracy = 2[( n +1)/2] ( n is a positive integer and [ · ] is the integral part of a number). We estimated the accuracy of three-point difference schemes and developed an algorithm for finding their solution. We also present the results of numerical experiments carried out to confirm our theoretical conclusions.
Bibliographie:ObjectType-Article-1
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ISSN:1072-3374
1573-8795
DOI:10.1007/s10958-023-06556-1