Nonlinear Relaxation Phenomena in Polycrystalline Solids

Numerical Solution of Telegraph Equation by Using LT Inversion Technique

“…Recently various powerful mathematical methods such as parameter-expansion method by Xu [17], variational iteration method by He [18], Exp-function method by Javidi and Golbabai [19], F-expansion method by He and Abdou [20], spectral domian decomposition approach by Golbabai and Javidi [21], and Nonlinear relaxation phenomena by Draganescu and Capalnasan [22], have been proposed to obtain exact and approximate analytic solutions for linear and nonlinear problems. The application of homotopy perturbation method in linear and nonlinear problems has been devoted by scientists and engineers, because this method is to continuously deform a simple problem which is easy to solve into the under study problem which is difficult to solve.…”

Numerical comparison for the solutions of anharmonic vibration of fractionally damped nano-sized oscillator

“…The mechanical properties of the micro-and nano-devices can be described in terms of classical or quantum mechanics (Cleland, 2003;Draganescu and Capalnasan, 2003;Draganescu, 2006;Dra˘ga˘nescu et al, 2010;Ke and Espinosa, 2004;Ghorbani and Nadjfi, 2007;He, 2008a). It is an established fact (Draganescu and Capalnasan, 2003;Draganescu, 2006;Dra˘ga˘nescu et al, 2010;Ke and Espinosa, 2004) that mechanical motion of the elements of micro-and nano-devices is examined inconnection with nonlinear forces of quantum nature similar to the Casimir force.…”

“…It is an established fact (Draganescu and Capalnasan, 2003;Draganescu, 2006;Dra˘ga˘nescu et al, 2010;Ke and Espinosa, 2004) that mechanical motion of the elements of micro-and nano-devices is examined inconnection with nonlinear forces of quantum nature similar to the Casimir force. Moreover, the anelastic properties of materials are nonlinear in nature (see Draganescu, 2006;Dra˘ga˘nescu et al, 2010;Ke and Espinosa, 2004;He, 2008a, and the references therein).…”

“…The Casimir effect consists in the electrical polarization of two perfectly conducting bodies, the Casimir force taking significant values when the separation between these bodies is reduced to less than 100 nm. On the other hand (Cleland, 2003;Draganescu and Capalnasan, 2003;Draganescu, 2006;Dra˘ga˘-nescu et al, 2010;Ke and Espinosa, 2004;Ghorbani and Nadjfi, 2007;He, 2008a), it was found that in materials like plastics and nano-wires, the most adequate kind of damping is the fractional damping. Recently, Dra˘ga˘nescu et al (2010) used Adomian's decomposition method for solving the governing problem.…”

The Homotopy Perturbation Method for Solving Nonlinear Burgers and New Coupled Modified Korteweg-de Vries Equations

“…Various methods for obtaining exact solutions to nonlinear partial differential equations have been proposed. Among these are the Bäcklund transformation method [1,2], the Hirota's bilinear method [3], the inverse scattering transform method [4], the extended tanh method [5 -7], the Adomian pade approximation [8 -10], the variational method [11 -14], the variational iteration method [15,16], the various Lindstedt-Poincare methods [17 -20], the Adomain decomposition method [8,21,22], the F-expansion method [23,24], the Exp-function method [25 -27] and others [28 -35].…”