Monotone iterates for systems of nonlinear integro-elliptic equations

Igor Boglaev

Abstract


This paper deals with numerically solving systems of nonlinear integro-elliptic equations. We give a monotone iterative method, based on the method of upper and lower solutions. The construction of the initial upper and lower solution is discussed, and numerical experiments are presented.

References
  • I. Boglaev, Numerical solving systems of nonlinear integro-parabolic equations of Volterra type. J. Integral Equ. Appl., 28(3):309–342, 2016. doi:10.1216/JIE-2016-28-3-1
  • C. V. Pao, Nonlinear Parabolic and Elliptic Equations. Plenum Press, New York, 1992.
  • C. V. Pao, Monotone iterative methods for numerical solutions of nonlinear integro-elliptic boundary problems. Appl. Math. Comput., 186:1624–1642, 2007. doi:10.1016/j.amc.2006.08.074
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  • A. H. Stroud, Approximate Calculation of Multiple Integrals. Prentice–Hall, Englewood Cliffs, New Jersey, 1971.

Keywords


integro-elliptic equations; monotone iterates; initial upper and lower solutions

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DOI: http://dx.doi.org/10.21914/anziamj.v58i0.11728



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