Spectral parameter power series representation for solutions of linear system of two first order differential equations

Nelson Gutiérrez Jiménez and Sergii M. Torba

Applied Mathematics and Computation, 2020, vol. 370, issue C

Abstract: A representation in the form of spectral parameter power series (SPPS) is given for a general solution of a one dimension Dirac system containing arbitrary matrix coefficient at the spectral parameter,BdYdx+P(x)Y=λR(x)Y,(*)where Y=(y1,y2)T is the unknown vector-function, λ is the spectral parameter, B=(01−10), and P is a symmetric 2 × 2 matrix, R is an arbitrary 2 × 2 matrix whose entries are integrable complex-valued functions. The coefficient functions in these series are obtained by recursively iterating a simple integration process, beginning with a non-vanishing solution for one particular λ=λ0. The existence of such solution is shown.

Keywords: Spectral parameter power series; Dirac system; Polya factorization; Sturm-Liouville spectral problem; Initial value problem; Numerical methods for ODE (search for similar items in EconPapers)
Date: 2020
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:370:y:2020:i:c:s0096300319309038

DOI: 10.1016/j.amc.2019.124911

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