Abstract
A system of nonlinear equations associated with finite-difference solution of problems of mathematical physics is considered. A so-called bounding linear system is constructed for the given nonlinear system. The solution accuracy of the bounding system is estimated by the magnitude of the discrepancy vector, which provides an estimate of the solution accuracy of the nonlinear system for the worst-case values of the nonlinear coefficients.
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E. K. Zaitsev, “Solving a system of nonlinear equations by isolating the constant component of the diagonal coefficients,” in: Computers in Modern Scientific-Technical Progress [in Russian], Vishcha Shkola, Kiev (1974), pp. 239–245.
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Translated from Vychislitel'naya i Prikladnaya Matematika, No. 58, pp. 24–28, 1986.
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Zaitsev, E.K. Accuracy of solution of some boundary-value problems of elasticity theory by finite-difference methods. J Math Sci 58, 408–411 (1992). https://doi.org/10.1007/BF01100065
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DOI: https://doi.org/10.1007/BF01100065