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Mathematical Problems in Engineering
Volume 2013, Article ID 643957, 2 pages

Numerical and Soft Computing Methods for Characteristic Value Problems of ODE and ODEs Systems

1Department of Mathematics, Nigde University, Central Campus, 51100 Nigde, Turkey
2Department of Economical, Juridical and Social Studies, University of Sannio, 82100 Benevento, Italy
3Department of Civil Engineering, Kocaeli University, Umuttepe Campus, 41380 Kocaeli, Turkey
4A-26 Sivasakthi Nagar, 7th Cross, Chidambaram, Tamil Nadu 608001, India
5Alanya Management Engineering Department, Akdeniz University, Kestel Campus, 07425 Alanya, Turkey
6Faculty of Economics and Business Sciences, University of Sannio, Via Delle Puglie 82, 82100 Benevento, Italy

Received 17 June 2013; Accepted 17 June 2013

Copyright © 2013 Mehmet Tarik Atay et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

1. Introduction

In many engineering and applied sciences fields, researchers encounter a special class of problems known as boundary value problems, or characteristic value problems. The desired or achieved solution for this kind of problems is required to satisfy given boundary conditions.

In real-world applications and their related problems, there are always some boundary conditions to meet for imitating the real case with simplified mathematical model with its boundary of initial conditions. Based on this idea, characteristic value problems of ODE and ODEs systems will always be a center of attention of scientific research.

Characteristic-value problems are a subset of boundary value problems because the governing ODE is a boundary value problem; except in characteristic value problems we are also concerned with the characteristic value, or eigenvalue, that governs the behavior of the boundary value problem.

The main focus of this special issue is on the novel analytical, numerical and soft computing methods and approaches which hopefully have potential value for researchers of characteristic value problems of ODE and ODEs systems and general characteristic value problems. The special issue has become an international forum for researchers to summarize the most recent developments and ideas in the field, with a special emphasis given to research results obtained within the last five years. The topics which are covered here in this special issue include below-mentioned research fields and related research titles. The special issue contains 14 original papers, selected by the editors so as to present the most significant results in general research fields given below.

2. Computational Solid Mechanics

There are 6 papers related to this field which are as follows: “Analytical solution for free vibration analysis of beam on elastic foundation with different support conditions” by B. Ozturk and S. B. Coskun, “Contact problem for an elastic layer on an elastic half plane loaded by means of three rigid flat punches” by T. S. Ozsahin and O. Taskıner, “Free vibration analysis of an euler beam of variable width on the Winkler foundation using homotopy perturbation method” by U. Mutman, “Sudden pressurization of a spherical cavity in a poroelastic medium”, by M. Ozyazicioglu, “Stability analysis of two-segment stepped columns with different end conditions and internal axial loads” by S. Pinarbasi, F. Okay, E. Akpinar, and H. Erdogan, “Application of adomian modified decomposition method to free vibration analysis of rotating beams” by Q. Mao.

3. Computational Heat Conduction and Fluid Mechanics

There are 3 papers related to this field which are as follows: “A spectral Solenoidal-Galerkin method for rotating thermal convection between rigid plates” by C. Yıldırım, D. Yarımpabuç, and H. I. Tarman, “Fourth-order deferred correction scheme for solving heat conduction problem” by D. Yambangwai and N. P. Moshkin, and “Approximation of first grade MHD squeezing fluid flow with slip boundary condition using DTM and OHAM” by I. Ullah, H. Khan, and M. T. Rahim.

4. Numerical and Soft Computing Methods for ODE and ODEs Systems and Related Fields

There are 5 papers related to this field which are as follows: “Some results on fuzzy soft topological spaces” by C. Gunduz (Aras) and S. Bayramov, “Homoclinic bifurcation and chaos in a noise-induced potential” by G. Ge, Z. Wen Zhu, and J. Xu, “The semianalytical solutions for stiff systems of ordinary differential equations by using variational iteration method and modified variational iteration method with comparison to exact solutions” by M. T. Atay and O. Kilic, “The approximate solutions of Fredholm integrodifferential-difference equations with variable coefficients via homotopy analysis method” by S. B. G. Karakoç, A. Eryılmaz, and M. Başbük, and “Asymptotic and numerical methods in estimating eigenvalues” by G. Yıldız, B. Yılmaz, and O. A. Veliev.

Mehmet Tarik Atay
Biagio Simonetti
Safa Bozkurt Coskun
D. Venkatesan
Murat Alper Basaran
Massimo Squillante