In this paper, we consider some blow-up properties of a semilinear heat equation, where the nonlinear term is of exponential type, subject to the zero Dirichletboundary conditions, defined in a ball in ?? ?? . Firstly, we study the blow-up set showing that the blow-up can only occur at a single point. Secondly, the upper blow-up rate estimate is derived.

Various iteration schemes are proposed by various authors to solve nonlinear equations arising in the implementation of implicit Runge-Kutta methods. In this paper, a class of s-step non-linear scheme based on projection method is proposed to accelerate the convergence rate of those linear iteration schemes. In this scheme, sequence of numerical solutions is updated after each sub-step is completed. For 2-stage Gauss method, upper bound for the spectral radius of its iteration matrix was obtained in the left half complex plane. This result is extended to 3-stage and 4-stage Gauss methods by transforming the coefficient matrix and the iteration matrix to a block diagonal form. Finally, some numerical experiments are carried out to confirm the obtained theoretical results.

The purpose of this paper is to introduce the notion of set-valued (??, ??)- weak contractions in cone metric spaces over Banach algebra and to prove some fixed point theorems for such mappings. The fixed point results of this paper generalize and extend several known fixed point results on cone metric spaces. An example in support of our results is given.

Throughout this paper simple and undirected graphs are considered. Let G = (V,E) be such a graph. The structure of a chemical compound can be represented by a graph whose vertex and edge specify the atom and bonds respectively. In this paper we compute certain topological indices of silicate chain.

The aim of this paper is to prove the existence common fixed point for compatible mapping of type (A) in Non-Archimedean Menger PM-space and we introduced new conditions for this type.