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Discontinuity, Nonlinearity, and Complexity

Dimitry Volchenkov (editor), Dumitru Baleanu (editor)

Dimitry Volchenkov(editor)

Mathematics & Statistics, Texas Tech University, 1108 Memorial Circle, Lubbock, TX 79409, USA


Dumitru Baleanu (editor)

Cankaya University, Ankara, Turkey; Institute of Space Sciences, Magurele-Bucharest, Romania


Using the Parameter Optimization Method for Solving Differential Equations with Contour Conditions: The nonlinear Euler-Bernoulli Beam

Discontinuity, Nonlinearity, and Complexity 8(4) (2019) 447--458 | DOI:10.5890/DNC.2019.12.008

Adélcio C. Oliveira

Departamento de Estatística, Física e Matemática, Universidade Federal de São João Del Rei C.P. 131, Ouro Branco, MG, 36420-000, Brazil

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The Parameter OptimizationMethod was presented with analytical and numerical examples. It was shown that it is a useful tool for solving differential equations with contour conditions. The numerical procedure is based only on Runge-Kutta integration routine and on optimization techniques, both frequently used and with many developed routines, thus it was shown that this approach is accessible and practical. The method was used to solve a one-dimensional Nonlinear Schr¨odinger Equation and a nonlinear Euler- Bernoulli beam.


The author gratefully acknowledge the support of Fundao de Amparo a Pesquisa do Estado de Minas Gerais (FAPEMIG) through grant No. APQ-01366-16. The author also acknowledge Marcelo O. Veloso and Maria T. M. Dias for their valuable comments and suggestions that helped to improve the quality of this work.


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