This paper presents a meshless point collocation method for three-dimensional crack propagation. The meshless point collocation method is based on direct discretization of strong-form governing equations to achieve a truly meshless scheme that does not require mesh structures or a numerical integration procedure. These characteristics of the point collocation method enable the direction of an a...

The utility of orthogonal collocation methods in the solution of optimal control problems relating to Formula One racing is demonstrated. These methods can be used to optimise driver controls such as the steering, braking and throttle usage, and the optimisation of vehicle parameters such as aerodynamic down force distributions. Of particular interest is the optimal usage of energy recovery sys...

We propose and analyze a numerical method for solving fourth order differential equations modelling two point boundary value problems. The scheme is based on B-splines collocation. The error analysis is carried out and convergence rates are derived.

Semiotic interpretation of lexical cohesion is a major research challenge both in theoretical and applied linguistics. From the point of view of usagebased language description, individual lexical units can be roughly characterized by their collocation profiles, i.e., by collections of condensed usage patterns extracted from very large corpora. It is posited that related lexical units tend to s...

Abstract We consider solitary-wave solutions of the generalized Burger’s-Fisher equation ∂Ψ ∂t + αΨ δ ∂Ψ ∂x − ∂ 2Ψ ∂x2 = βΨ(1 − Ψδ). In this paper, we present a new method for solving of the generalized Burger’s-Fisher equation by using the collocation formula for calculating spectral differentiation matrix for Chebyshev-Gauss-Lobatto point. To reduce round-off error in spectral collocation met...

The purpose of the present study is to investigate the boundary layer separation point in a magnetohydrodynamics diffuser. As an innovation, the Re value on the separation point is determined for the non-Newtonian fluid flow under the influence of the non-uniform magnetic field due to an electrical solenoid, in an empirical case. The governing equations include continuity and momentum are solve...

An algorithm is described for the efficient numerical solution of singular two-point boundary value problems. The algorithm is based on collocation at Gauss points, is applied directly to second order equations and uses a transformation of the independent variable to obtain extra smoothness if needed. Numerical comparisons between a code based on this approach and codes based on other options w...