Lanczos τ-method optimal algorithm in APS for approximating the mathematical functions

2006/03/26 by Denisenko, P. N.
#Classical Analysis and ODEs (math.CA) #FOS: Computer and information sciences #FOS: Mathematics #Mathematical Software (cs.MS) #Numerical Analysis (math.NA)

paper · doi:10.48550/arxiv.math/0603606

Abstract

A new procedure is constructed by means of APS in APLAN language. The procedure solves the initial-value problem for linear differential equations of order k with polynomial coefficients and regular singularity in the initialization point in the interval [a, b] and computes the algebraic polynomial y_n of given order n. A new algorithm of Lanczos τ-method is built for this procedure, the solution existence y_n of the initial-value problem proved on this algorithm and also is proved the optimality by precision of order k derivative of the initial-value problem solution.

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