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Exact solution of the harmonic problem for a rectangular plate in flat deformation by the method of initial functions

Olodo E. T., Adanhounme V., Hounkonnou M. N.

International Journal of Applied Mechanics and Engineering

2017

Vol. 22, no. 2

349--361

A wide range of applications is based nowadays on analytical developments which allow a precise and effective approach and short time of computations compared with the time required for numerical methods; in this way these developments are suitable for calculations in real time. This work proposes an approach for solving a two-dimensional harmonic problem of a rectangular plate under local surface loading using Vlasov’s symbolic method of initial functions and a general solution of the harmonic equation for a rectangle. Substituting the harmonic functions in symbolic form for the corresponding solutions allows us to give the exact solution of the problem in trigonometric form.

Single-valley-extended continuous solutions for the Feigenbaum's functional equation f (φ(x)) = φ2(f(x))

Zhang M.

Demonstratio Mathematica

2014

Vol. 47, nr 3

615--626

This work deals with the Feigenbaum's functional equation in the broad sense (…), where φ2 is the 2-fold iteration of φ, f(x) is a strictly increasing continuous function on [0, 1] and satisfies (...). Using constructive method, we discuss the existence of single-valley-extended continuous solutions of the above equation.