Journal of Applied & Computational Mathematics

ISSN: 2168-9679

Open Access

Volume 5, Issue 5 (2016)

Research Article Pages: 1 - 4

Stability of Fourier Solutions of Nonlinear Stochastic Heat Equations in 1D

Hazaimeh MH

DOI: 10.4172/2168-9679.1000323

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.

Research Article Pages: 1 - 7

Diagonally Implicit Super Class of Block Backward Differentiation Formula with Off?¢???Step Points for Solving Stiff Initial Value Problems

Babangida B and Musa H

DOI: 10.4172/2168-9679.1000324

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.

Research Article Pages: 1 - 6

Seeing as Understanding: The Importance of Visual Mathematics for our Brain and Learning

Jo Boaler, Lang Chen, Cathy Williams and Montserrat Cordero

DOI: 10.4172/2168-9679.1000325

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?

Research Article Pages: 1 - 7

The k-out-of-n System Model with Degradation Facility

El-Damcese MA and Shama MS

DOI: 10.4172/2168-9679.1000326

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.

Research Article Pages: 1 - 7

Application of Septic B-Spline Collocation Method for Solving the Coupled-BBM System

Raslan KR, EL-Danaf TS and Ali KK

DOI: 10.4172/2168-9679.1000327

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.

Short Communication Pages: 1 - 2

Two News Approximations to Standard Normal Distribution Function

Abderrahmane M and Boukhetala Kamel B

DOI: 10.4172/2168-9679.1000328

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.

Research Article Pages: 1 - 6

Characterizations of Certain Doubly Truncated Distribution Based on Order Statistics

Shawky AI and Badr MM

DOI: 10.4172/2168-9679.1000329

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.

Research Article Pages: 1 - 3

Convergence of the 2-Point Diagonally Implicit Super Class of BBDF with Off?¢???Step Points for Solving Stiff IVPs

Babangida B and Hamisu M

DOI: 10.4172/2168-9679.1000330

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.

Research Article Pages: 1 - 7

The New Generalized Difference Sequence Space ???2 over p?¢?????Metric Spaces Defined by Musielak Orlicz Function Associated with a Sequence of Multipliers

Deepmala, Subramanian N and Mishra LN

DOI: 10.4172/2168-9679.1000331

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.

Google Scholar citation report
Citations: 1282

Journal of Applied & Computational Mathematics received 1282 citations as per Google Scholar report

Journal of Applied & Computational Mathematics peer review process verified at publons

Indexed In

arrow_upward arrow_upward