We propose a discrete collocation method for the boundary integral equations which arise from solving Laplace's equation u = 0. The Laplace's equation is deened on connected regions D in R 3 with a smooth boundary S. The piecewise polynomial interpolation in the parametrization variables along with the collocation method is used, and a numerical integration scheme for collocation integrals is g...

in this paper we use radial basis functions to solve multivariable integral equations. we use collocation method for implementation. numerical experiments show the accuracy of the method.

objective(s):breast cancer is an important leading cause of death from cancer. stathmin and tau proteins are regulators of cell motility, and their overexpression is associated with the progression and bad prognosis of breast cancer. memantine, an n-methyl-d-aspartate (nmda) receptor antagonist, is the potential inhibitor of tau protein in neurons. this study determines the effect of memantine ...

The Meshless Local Petrov-Galerkin (MLPG) “mixed collocation” method is applied to the problem of topology-optimization of elastic structures. In this paper, the topic of compliance minimization of elastic structures is pursued, and nodal design variables which represent nodal volume fractions at discretized nodes are adopted. A so-called nodal sensitivity filter is employed, to prevent the phe...

In this article, we have investigate a Taylor collocation method, which is based on collocation method for solving fractional pantograph equation. This method is based on first taking the truncated fractional Taylor expansions of the solution function in the mathematical model and then substituting their matrix forms into the equation. Using the collocation points, we have the system of nonline...

Almost nothing decisive has been said about collocation methods for solving SPDEs. Among the best of such SPDEs the Burgers equation shows a prototypical model for describing the interaction between the reaction mechanism, convection effect, and diffusion transport. This paper discusses spectral collocation method to reduce stochastic Burgers equation to a system of stochastic ordinary differen...

Herein, two numerical algorithms for solving some linear and nonlinear fractional-order differential equations are presented and analyzed. For this purpose, a novel operational matrix of fractional-order derivatives of Fibonacci polynomials was constructed and employed along with the application of the tau and collocation spectral methods. The convergence and error analysis of the suggested Fib...

Collocation has always been an important issue in language research, especially in Chinese language researches. Chinese is an isolated language, which lacks morphological changes.Establishing a relatively complete dictionary of Chinese collocation will be a great contribution to Chinese study and research. Collocation plays a significant supporting role in many fields of NLP, such as informatio...

We rigorously study a novel type of trigonometric Fourier collocation methods for solving multi-frequency oscillatory second-order ordinary differential equations (ODEs) q′′(t) + Mq(t) = f(q(t)) with a principal frequency matrix M ∈ Rd×d. If M is symmetric and positive semi-definite and f(q) = −∇U(q) for a smooth function U(q), then this is a multi-frequency oscillatory Hamiltonian system with ...

Here we propose a new method based on projections for the approximate solution of eigenvalue problems. For an integral operator with a smooth kernel, using an interpolatory projection at Gauss points onto the space of (discontinuous) piecewise polynomials of degree ≤ r−1, we show that the proposed method exhibits an error of the order of 4r for eigenvalue approximation and of the order of 3r fo...