Abstract
In this paper, we construct the conservative spectral scheme for the periodic initial-value problem for a system of equations of the complex Schrödinger field, interacting with the real Klein—Gordon field and estimate the error which is \\xV;\\GF;( nk) − Φ n N \\xV; + \\xV;χ( nk) − iX n n\\xV; 1 = O( k 2 + N −(γ−1)).
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