Rank of Projection-Algebraic Representations of Some Differential Operators - Mathematics > Classical Analysis and ODEsReport as inadecuate




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Abstract: The Lie-algebraic method approximates differential operators that are formalpolynomials of {1,x,d-dx} by linear operators acting on a finite dimensionalspace of polynomials. In this paper we prove that the rank of the n-dimensionalrepresentation of the operator K=a k d^k-dx^k+a {k+1} d^{k+1}-dx^{k+1}+

.+a {k+p} d^{k+p}-dx^{k+p} is n-k and conclude that the Lie-algebraic reductionsof differential equations allow to approximate only some of solutions of thedifferential equation Ku=f. We show how to circumvent this obstacle whensolving boundary value problems by making an appropriate change of variables.We generalize our results to the case of several dimensions and illustrate themwith numerical tests.



Author: Oksana Bihun, Mykola Prytula

Source: https://arxiv.org/







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