Monotone iterates for systems of nonlinear integro-elliptic equations

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 A. Samarskii, The Theory of Difference Schemes . Marcel Dekker, New York, 2001. A. H. Stroud, Approximate Calculation of Multiple Integrals . Prentice–Hall, Englewood Cliffs, New Jersey, 1971.