Summary.
We examine the use of orthogonal spline collocation for the semi-discreti\-za\-tion of the cubic Schr\"{o}dinger equation and the two-dimensional parabolic equation of Tappert. In each case, an optimal order\(L^2\) estimate of the error in the semidiscrete approximation is derived. For the cubic Schr\"{o}dinger equation, we present the results of numerical experiments in which the integration in time is performed using a routine from a software library.
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Received February 14, 1992 / Revised version received December 29, 1992
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Robinson, M., Fairweather, G. Orthogonal spline collocation methods for Schr\"{o}dinger-type equations in one space variable . Numer. Math. 68, 355–376 (1994). https://doi.org/10.1007/s002110050067
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DOI: https://doi.org/10.1007/s002110050067