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

We consider Hammerstein equations of the form y(i)=f(t)+(hk(t,s)g(s,y(s))ds, te[a,b], J a and present a new method for solving them numerically. The method is a collocation method applied not to the equation in its original form, but rather to an equivalent equation for z(t):= g(t,y(t)). The desired approximation to y is then obtained by use of the (exact) equation y(t)=f(t) + fh k(t,s)z(s)ds, ...

Simplest results presented here are the stability criteria of collocation methods for the second-order Volterra integrodifferential equation (VIDE) by polynomial spline functions. The polynomial spline collocation method is stable if all eigenvalues of a matrix are in the unit disk and all eigenvalues with |λ| = 1 belong to a 1× 1 Jordan block. Also many other conditions are derived depending u...

pollution has become a very serious threat to our environment. monitoring pollution is the rst step toward planning to save the environment. the use of dierential equations, monitoring pollution has become possible. in this paper, a ritz-collocation method is introduced to solve non-linear oscillatory systems such as modelling the pollution of a system of lakes. the method is based upon bernoul...

in this paper, a new spectral-iterative method is employed to give approximate solutions of fractional logistic differential equation. this approach is based on combination of two different methods, i.e. the iterative method cite{35} and the spectral method. the method reduces the differential equation to systems of linear algebraic equations and then the resulting systems are solved by a numer...