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Zbl 1231.45016
Al-Mdallal, Qasem M.
Monotone iterative sequences for nonlinear integro-differential equations of second order. (English)
[J] Nonlinear Anal., Real World Appl. 12, No. 6, 3665-3673 (2011). ISSN 1468-1218

Summary: We present an efficient algorithm based on a monotone method for the solution of a class of nonlinear integro-differential equations of second order. This method is applied to derive two monotone sequences of upper and lower solutions which are uniformly convergent. Theorems which list the conditions for the existence of such sequences are presented. The numerical results demonstrate reliability and efficiency of the proposed algorithm.

MSC 2000:: *45J05 Integro-ordinary differential equations
34K10 Boundary value problems for functional-differential equations

Keywords: nonlinear integro-differential equations; maximum principle; monotone method; lower and upper solutions

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