The Meshless Local Petrov-Galerkin (MLPG) mixed collocation method is proposed in this paper, for solving elasticity problems. In the present MLPG approach, the mixed scheme is applied to interpolate the displacements and stresses independently, as in the MLPG finite volume method. To improve the efficiency, the local weak form is established at the nodal points, for the stresses, by using the ...

Three different spline-based approaches for solving Bratu and Bratu-type equations are presented. The classical cubic spline collocation method, an adaptive spline collocation on nonuniform partitions, and an optimal collocation method are derived for solving Bratu-type equations. Numerical examples are presented to verify the efficiency and accuracy of these methods when compared to other nume...

We have suggested the numerical schemes of collocation methods and mechanical quadrature methods for approximative solution of singular integro-differential equations with kernels of Cauchy type. The equations are defined on the arbitrary smooth closed contours of complex plane. The researched methods are based on the descritization by Fejér points. Theoretical background for collocation method...

To apply satellite-retrieved soil moisture to a short-range weather prediction, we review a stochastic approach for reducing foot print scale biases and estimating its uncertainties. First, we discuss a challenge of representativeness errors. Before describing retrieval errors in more detail, we clarify a conceptual difference between error and uncertainty in basic metrological terms of the Int...

The Lane-Emden equation has been used to model several phenomenas in theoretical physics, mathematical physics and astrophysics such as the theory of stellar structure. This study is an attempt to utilize the collocation method with the Rational Chebyshev of Second Kind function (RSC) to solve the Lane-Emden equation over the semi-infinit interval [0,+∞). According to well-known results and com...

We have suggested the numerical schemes of collocation methods for approximative solution of singular integrodifferential equations with kernels of Cauchy type. The equations are defined on the arbitrary smooth closed contours of complex plane. The researched methods are based on Fejér points. Theoretical background of collocation methods has been obtained in Generalized Hölder spaces. Singular...

we present a collocation method to obtain the approximate solutionof troesch's problem which arises in the confinement of a plasmacolumn by radiation pressure and applied physics. by using thechristov rational functions and collocation points, this methodtransforms troesch's problem into a system of nonlinear algebraicequations. the rate of convergence is shown to be exponential. then...

In this paper, the orthogonal collocation technique is utilized to solve the Poppe method equations for heat and mass transfer in counter flowing wet-cooling towers. The six differential equations for unsaturated and supersaturated air from the Poppe method are simplified, yielding three differential equations that use the Heaviside function. The humidity ratio is demonstrated to be a finite po...

1 King Abdulaziz University, Faculty of Science, Department of Mathematics, Jeddah, Saudi Arabia 2 Beni-Suef University, Faculty of Science, Department of Mathematics, Beni-Suef, Egypt 3 King Abdulaziz University, Department of Chemical and Materials Engineering, Faculty of Engineering, Jeddah, Saudi Arabia 4 Cankaya University, Faculty of Arts and Sciences, Department of Mathematics and Comput...

Solutions of partial differential equations with coordinate singularities often have special behavior near the singularities, which forces them to be smooth. Special treatment for these coordinate singularities is necessary in spectral approximations in order to avoid degradation of accuracy and efficiency. It has been observed numerically in the past that, for a scheme to attain high accuracy,...