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Zbl 1114.65159
West, Ianna H.; Watsala, A.S.
Generalized monotone iterative method for integro differential equations with periodic boundary conditions. (English)
[J] Math. Inequal. Appl. 10, No. 1, 151-163 (2007). ISSN 1331-4343

The authors develop a generalized monotone iterative method for first-order nonlinear integro-differential equations with periodic boundary conditions when the forcing function is the sum of an increasing and decreasing function. Monotone or alterning monotone sequences are obtained. They depend on the coupled upper and lower solution used and on the iterative scheme. These sequences converge to coupled external solutions of the equation.\par Numerical results are given.
[Yves Cherruault (Paris)]

MSC 2000:: *65R20 Integral equations (numerical methods)
45J05 Integro-ordinary differential equations
45G10 Nonsingular nonlinear integral equations

Keywords: periodic boundary condition; convergence; first-order nonlinear integro-differential equations; upper and lower solution

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Zentralblatt MATH Berlin [Germany]