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- W2990675571 abstract "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, B d Y d x + P ( x ) Y = λ R ( x ) Y , ( * ) where Y = ( y 1 , y 2 ) T is the unknown vector-function, λ is the spectral parameter, B = ( 0 1 − 1 0 ) , 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 = λ 0 . The existence of such solution is shown. For a general linear system of two first order differential equations P ( x ) d Y d x + Q ( x ) Y = λ R ( x ) Y , x ∈ [ a , b ] , where P, Q, R are 2 × 2 matrices whose entries are integrable complex-valued functions, P being invertible for every x, a transformation reducing it to a system (*) is shown. The general scheme of application of the SPPS representation to the solution of initial value and spectral problems as well as numerical illustrations are provided." @default.
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- W2990675571 date "2020-04-01" @default.
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- W2990675571 title "Spectral parameter power series representation for solutions of linear system of two first order differential equations" @default.
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