In this paper, a new collocation method, which is based on Boubaker polynomials, is introduced for the approximate solutions of a class of two-dimensional linear Fredholm integral equationsof the second kind. The properties of two-dimensional Boubaker functions are presented. The fundamental matrices of integration with the collocation points are utilized to reduce the solution of the integral ...

This paper presents a class of efficient Newton-type algorithms for solving the nonlinear programs (NLPs) arising from applying a direct collocation approach to continuous time optimal control. The idea is based on an implicit lifting technique including a condensing and expansion step, such that the structure of each subproblem corresponds to that of the multiple shooting method for direct opt...

In the present work, the mathematical model of a homogeneous, isotropic thermoelastic double porous micro-beam, based on the Euler-Bernoulli theory is developed in the context of Lord-Shulman [1] theory of thermoelasticity. Laplace transform technique has been used to obtain the expressions for lateral deflection, axial stress, axial displacement, volume fraction field and temperature distribut...

The displacement response of structures can provide important information regarding their behaviours. Since image-based measurements have been considerably improved in recent years, this research, a fiducial marker-based approach is exploited and measurement technique proposed. With method, an industrial camera be used to measure the structure through detection ArUco marker. A comparison with e...

Among fitted-operator methods for solving one-dimensional singular perturbation problems one of the most accurate is the collocation by linear combinations of {1, x, exp (±px)}, known as tension spline collocation. There exist well established results for determining the ‘tension parameter’ p, as well as special collocation points, that provide higher order local and global convergence rates. H...