Journal of Applied & Computational Mathematics

The main focus of this article is studying the stability of solutions of nonlinear stochastic heat equation and give conclusions in two cases: stability in probability and almost sure exponential stability. The main tool is the study of related Lyapunov-type functionals. The analysis is carried out by a natural N-dimensional truncation in isometric Hilbert spaces and uniform estimation of moments with respect to N.

Nonlinear stochastic heat equation, additive space-time noise, Lyapunov functional, Fourier solution, finitedimensional approximations, moments, stability.

A new formula called 2-point diagonally implicit super class of BBDF with two off-step points (2ODISBBDF) for solving stiff IVPs is formulated. The method approximates two solutions with two off-step points simultaneously at each iteration. By varying a parameter ρ ∈ (–1,1) in the formula, different sets of formulae can be generated. A specific choice of ρ =3/4  is made and it was shown that the method is both zero and A-stable. A comparison between the new method and the existing 2-point block backward differentiation formula with off-step points (2OBBDF) is made. The results show that the new method outperformed existing 2OBBDF method in terms of accuracy.

A few weeks ago the silence of my Stanford office was interrupted by a phone call. A mother called to tell me that her 5-year old daughter had come home from school crying because her teacher had not allowed her to count on her fingers. A few weeks afterwards, when I told my undergraduate mathematics class that visual mathematics was really important, one of them asked: but it is only for low levels of math, isn’t it?

In this paper, we study the reliability analysis of k-out-of-n system with degradation facility. Let failure rate, degradable rate and repair rate of components are assumed to be exponentially distributed. There are two types of repair. The first is due to failed state. The second is due to degraded state. The expressions of reliability and mean time to system failure are derived with repair and without repair. We used several cases to analyze graphically the effect of various system parameters on the reliability system.

In the present paper, a numerical method is proposed for the numerical solution of a coupled-BBM system with appropriate initial and boundary conditions by using collocation method with septic B-spline on the uniform mesh points. The method is shown to be unconditionally stable using von-Neumann technique. To test accuracy the error norms L2, L∞ are computed. Furthermore, interaction of two and three solitary waves are used to discuss the effect of the behavior of the solitary waves after the interaction. These results show that the technique introduced here is easy to apply. We make linearization for the nonlinear term.

This paper, presents two news approximations to the Cumulative Distribution Function (CDF). The first approximation 22 improves the accuracy of approximation given by Hart. In this first new approximation, we reduce the maximum absolute error (MAE) from, 0.004304 to 2.707e-004.For the second new approximation, Aludaat and Alodat was reduce the (MAE) from, 0.00314 to 0.001972. In this paper, we reduce the (MAE) to 0.001623. However, the first approximation is more accurate and its inverse is hard to calculate. The second new approximation is less accurate, but his inverse is easy to calculate.

In this paper, we characterize doubly truncated classes of absolutely continuous distributions by considering the conditional expectation of functions of order statistics. Specific distributions considered as a particular case of the general class of distributions are Weibull, Pareto, Power function, Rayleigh and Inverse Weibull.

The 2-point Diagonally Implicit Superclass of BBDF with off-step point’s method proposed by Babangida had been studied and further established the necessary conditions for its convergence. Consistency, zero stability and order of the method are discussed.

In the present paper, we introduce new sequence spaces by using Musielak-Orlicz function and a generalized -difference operator on p–metric space. Some topological properties and inclusion relations are also examined.