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Approximate method for boundary value problems of anti-periodic type for differential equations with ‘maxima’

Snezhana Hristova*, Angel Golev and Kremena Stefanova

Author Affiliations

Faculty of Mathematics and Informatics, Plovdiv University, Plovdiv, 4000, Bulgaria

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Boundary Value Problems 2013, 2013:12  doi:10.1186/1687-2770-2013-12

Published: 25 January 2013


An algorithm for constructing two sequences of successive approximations of a solution of the nonlinear boundary value problem for a nonlinear differential equation with ‘maxima’ is given. The case of a boundary condition of anti-periodic type is investigated. This algorithm is based on the monotone iterative technique. Two sequences of successive approximations are constructed. It is proved both sequences are monotonically convergent. Each term of the constructed sequences is a solution of an initial value problem for a linear differential equation with ‘maxima’ and it is a lower/upper solution of the given problem. A computer realization of the algorithm is suggested and it is illustrated on a particular example.

MSC: 34K10, 34K25, 34B15.

differential equations with ‘maxima’; nonlinear boundary value problem; approximate solution; computer realization