Zeitschrift für Angewandte und Computermathematik

The paper discusses the error estimate of Wu-Schaback's quasi-interpolant for a wider class of approximated functions (the functions with lower smoothness order). Three cases are considered: a function with a Lipschitz continuous first-order derivative, a continuous function and a Lipschitz continuous function, respectively.

Stability and practically stability comparison criteria of impulsive integro-differential systems with fixed moments of impulse effects are established by cone-Lyapunov functions through comparing with impulsive ordinary differential equations.

We propose to contribute to the emerging body of cancer treatment research by developing and analyzing mathematical models of the treatment of tumor with various strategic treatments. We build on existing models of the immunology that are already successfully developed and then the effects of chemotherapy and interleukin-2 were applied to the model. Thus we build a mathematical model of tumour and effector cell with scheduled chemotherapy. The effect of scheduled il2 dose with chemotherapy and adoptive immunotherapy reduced the tumor growth.

In this paper, we proposed a new method for the numerical solutions of a two-dimensional Poisson equation, where we used k-modes clustering algorithm to improve the standard five-point difference scheme. Numerical experiments have shown that the five-point difference method based on k-modes cluster is effective and efficient. The proposed new method not only reduces computing time remarkably, but also shows better performance in data storage and stability than the standard five-point difference scheme.

Studying the synaptic signal transmission in the neuromuscular junction (NMJ) is central to the understanding of neuromuscular disorders such as myasthenia gravis disease. Investigating the dynamics of acetylcholine and acetylcholine receptors in an NMJ under the conditions of activated enzyme is an important step towards this mission. In this article, we developed a numerical model of high order accuracy for complex geometry to simulate the complex processes in an NMJ cleft. This model has a full description of three-dimensional reaction and diffusion processes with nonlinear reaction source terms and is capable of predicting the concentration rates of acetylcholine with receptors and enzymes. Simulation results agree with experimental measurement of the reported maximum number of open receptors during the course of a normal action potential. The time variation of populations of open receptor as well as concentration rates are investigated and discussed. This model has the potential to further the in depth investigation of dynamics within an NMJ.

We developed a one step-three hybrid point constant order predictor corrector method for the solution of general third order initial value problems. The method was developed using method of interpolation and collocation of power series approximate solution to generate a continuous linear multistep method which was evaluated at some selected grid point to give the discrete linear multistep method. The predictors are implemented in block method while the corrector gave the solution at an overlapping interval. The basic properties of both the corrector and the predictors were investigated and found to be zero stable, consistent and convergent. The region of absolute stability was also investigated. The efficiency of the derived method was tested on some numerical examples and found to compete favourably with the existing methods.

In this paper we introduce certain new subclasses of uniformly p-valent star like and convex functions. Sufficient coefficient conditions are obtained for functions in these classes. We provide geometrical properties of functions belonging to these classes. Hadamard product with convex functions and certain coefficient estimates are also obtained.

In this paper, we investigate some new criteria on the asymptotic behavior of non-oscillatory solutions of second order integro-dynamic equations on time-scales. We also provide some numerical examples to illustrate the relevance of the obtained results.