An efficient method for oxygen diffusion in a spherical cell with nonlinear oxygen uptake kinetics

In this paper, a novel numerical technique, the first-order Smooth Composite Chebyshev Finite Difference method, is presented. Imposing a first-order smoothness of the approximation polynomial at the ends of each subinterval is originality of the method. Both round-off and truncation error analyses of the method are performed beside the convergence analysis. Diffusion of oxygen in a spherical cell including nonlinear uptake kinetics is solved by using the method. The obtained results are compared with the existing methods in the literature and it is observed that the proposed method gives more reliable results.

Image Compression and Enlargement Algorithms

In some cases, there are problems associated with the compression and enlargement of images. The use of splines is quite effective in some cases. In this paper, a new image compression algorithm is presented. The features of increasing the size of an image when using local polynomial or non-polynomial splines are considered. The main method for enlarging an image is based on the use of splines of the second and third order of approximation. Polynomial and trigonometric splines are considered. To speed up the process of enlarging the image, we used the parallelization techniques

First order smooth composite Chebyshev finite difference method for solving coupled Lane-Emden problem in catalytic diffusion reactions

A new effective technique based on Chebyshev Finite Difference Method is introduced. First order smoothness of the approximation polynomial at the end points of each sub-interval is imposed in addition to the continuity condition. Both round-off and truncation error analyses are given besides the convergence analysis. Coupled Lane Emden boundary value problem in Catalytic Diffusion Reactions is investigated by using presented method. The obtained results are compared with the existing methods in the literature and it is observed that the proposed method gives more reliable results than the others.

Approximation by the Third-Order Splines on Uniform and Non-uniform Grids and Image Processing

This work is one of a series of papers that is devoted to the further investigation of polynomial splines and trigonometric splines of the third order approximation. Polynomial basis splines are better known and therefore more commonly used. However, the use of trigonometric basis splines often provides a smaller approximation error. In some cases, the use of the trigonometric approximations is preferable to the polynomial approximations. Here we continue to compare these two types of approximation. The Lebesgue functions and constants are discussed for the polynomial splines and the trigonometric splines. The examples of the applications of the splines to image enlargement are given.