An error analysis of iterated defect correction methods for linear differential-algebraic equations

Asymptotic expansions of the global error of iterated defect correction (IDeC) techniques based on the implicit Euler method for linear differential-algebraic equations (dae's) of arbitrary index are analyzed. The dependence of the maximum attainable convergence order on the degree of the interpolating polynomial, number of defect correction steps, and on the index of the differential-algebraic system is given. The efficiency of IDeC method and extrapolation is compared on the basis of numerical experiments and comparing computational cost for both methods. Linear time-varying differential-algebraic equations are investigated by presenting numerical results and extending theoretical results for constant coefficient to these problems.


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Bayin, Selcuk S. (2012-08-01)
Recently we have reanalyzed the consistency of the solutions of the space fractional Schroumldinger equation found in a piecewise manner, and showed that an exact and a proper treatment of the relevant integrals prove that they are consistent. In this comment, for clarity, we present additional information about the critical integrals and describe how their analytic continuation is accomplished.
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In this thesis, the theory of the relations between differential and integral equations is analyzed and is illustrated by the reformulation of the one-dimensional Schrödinger equation in terms of an integral equation employing the Green’s function. The Rayleigh- Ritz method is applied to the integral-equation formulation of the one-dimensional Schrödinger equation in order to approximate the eigenvalues of the corresponding singular problem within the desired accuracy. The outcomes are compared with those r...
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Citation Formats
B. Karasözen, “An error analysis of iterated defect correction methods for linear differential-algebraic equations,” INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS, pp. 121–137, 1996, Accessed: 00, 2020. [Online]. Available: