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,...

P variety is an important strategic tool that firms can use to attract customers and respond to competition. This study focuses on the retail industry and investigates how stores manage their product variety, contingent on the presence of competition and their actual distance from rivals. Using a unique data set that contains all Best Buy and Circuit City stores in the United States, the author...

The aim of this paper is to solve the second order neutral delay differential equations (NDDEs) based on seventh C3-spline collocation methods with three parameters c1, c2, c3 ∈ (0, 1). It is shown that the proposed methods for second order NDDEs possess a convergence rate of order seven if : 1− c1 − c2 − c3 + c1c2 + c1c3 + c2c3 − 2c1c2c3 ≤ 0. Numerical results illustrating the behavior of the ...

Fast Algorithms with Applications to PDEs