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

Autor:	Kunynets, A. V., Kutniv, M. V., Khomenko, N. V.
Předmět:	LINEAR differential equations RUNGE-Kutta formulas TAYLOR'S series CAUCHY problem NEWTON-Raphson method ORDINARY differential equations INTEGRALS
Zdroj:	Journal of Mathematical Sciences; Jul2023, Vol. 273 Issue 6, p948-959, 12p
Abstrakt:	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 xj , j = 1,2,...,N − 1, require solving of two Cauchy problems for the second-order linear ordinary differential equations on the segments [xj−1, xj] (forward) and [xj , xj+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. [ABSTRACT FROM AUTHOR]
Databáze:	Complementary Index
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