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Research ArticleOpen accessEvery word in the titleSOME STATISTICAL PROPERTIES OF THE SOLUTIONS OF A SYSTEM OF TWO DIMENSIONAL STOCHASTIC FREDHOLM INTEGRAL EQUATIONS CONTAINS GAMMA PROCESSESMohammad Wahdan MuflihIn this study, we find the two solutions of a system of two dimensional stochastic Fredholm integral equations contains two gamma processes with different values of the two parameters (the first controls the rate of jump arrivals and the second inversely controls the jump size of this arrivals) in two cases and equal in the third that is to introduce … …Journal of Mathematics and Statistics, Vol. 9, Issue 2 · 4 May 2013 · 6,900 accessesView PDFCite
Research ArticleOpen accessEvery word in the titleDynamics of Coherent Structures in the Coupled Complex Ginzburg-Landau EquationsTat-Leung YeeProblem statement: In this study, we study the analytical construction of some exact solutions of a system of coupled physical differential equations, namely, the Complex Ginzburg-Landau Equations (CGLEs). CGLEs are intensively studied models of pattern formation in nonlinear dissipative media, with applications to biology, hydrodynamics, nonlinear optics, plasma physics, reaction-diffusion systems and many other fields. Approach: A system of two … …Journal of Mathematics and Statistics, Vol. 8, Issue 3 · 6 Nov 2012 · 6,994 accessesView PDFCite
Research ArticleOpen accessEvery word in the titleTime-Delay Estimation using the Characteristic Roots of Delay Differential EquationsSun Yi, Wonchang Choi, Taher Abu-LebdehProblem statement: For ordinary dynamic systems (i.e., non-delayed), various methods such as linear least-squares, gradient-weighted least-squares, Kalman filtering and other robust techniques have been widely used in signal processing, robotics, civil engineering. On the other hand, time-delay estimation of systems with unknown time-delay is still a challenging problem due to difficulty in formulation caused. Approach: The presented method makes use … …American Journal of Applied Sciences, Vol. 9, Issue 6 · 7 Apr 2012 · 8,090 accessesView PDFCite
Research ArticleOpen accessEvery word in the titleAn Embedded Explicit Hybrid Method for Ordinary Differential EquationsF. Samat, F. IsmailProblem statement: Many differential systems that appear in practice were special second-order ordinary differential equations of the form y" = f (x, y). In the past research, there was a continuous need for methods for numerically solving these equations. Approach: This study describes the derivation and implementation of a pair of embedded explicit hybrid methods for solving non-stiff second-order ordinary … …Journal of Mathematics and Statistics, Vol. 8, Issue 1 · 23 Dec 2011 · 7,423 accessesView PDFCite
Research ArticleOpen accessEvery word in the titleA New Newton's Method with Diagonal Jacobian Approximation for Systems of Nonlinear EquationsM. Y. Waziri, W. J. Leong, M. A. Hassan, M. MonsiProblem statement: The major weaknesses of Newton method for nonlinear equations entail computation of Jacobian matrix and solving systems of n linear equations in each of the iterations. Approach: In some extent function derivatives are quit costly and Jacobian is computationally expensive which requires evaluation (storage) of n×n matrix in every iteration. Results: This storage requirement became unrealistic when n … …Journal of Mathematics and Statistics, Vol. 6, Issue 3 · 30 Sep 2010 · 8,541 accessesView PDFCite
Research ArticleOpen accessEvery word in the titleCost Analysis of K-Out of-n Repairable System with Dependent Failure and Stand by Support Using Kolmogorov's Forward Equations MethodM. Y. HaggagProblem statement: Many authors have studied k-out of-n repairable system with dependent failure and standby support. The question was raised whether the repair and standby units support increase the reliability of the system. Determine the efficiency of repair and standby support on the reliability of the system. Approach: In this study the statistical analysis of k-out of-n repairable system with … …Journal of Mathematics and Statistics, Vol. 5, Issue 4 · 31 Dec 2009 · 6,603 accessesView PDFCite
Research ArticleOpen accessEvery word in the titleCost Analysis of Two-Dissimilar-Unit Cold Standby System with three States and Preventive Maintenance Using Linear First Order Differential EquationsM. Y. HaggagProblem statement: Several researchers have studied the reliability behavior of a three state systems, but no attention was paid to the reliability evaluation due to preventive maintenance. The better maintenance of the system originates better reliability. Also, standby support increases the reliability of the system. Approach: Determine the efficacy of preventive maintenance on the reliability and performance of the system. … …Journal of Mathematics and Statistics, Vol. 5, Issue 4 · 31 Dec 2009 · 6,881 accessesView PDFCite
Research ArticleOpen accessEvery word in the titleOn the Pseudo-Spectral Method of Solving Linear Ordinary Differential EquationsB. S. OgundareProblem statement: Not all differential equations can be solved analytically, to overcome this problem, there is need to search for an accurate approximate solution. Approach: The objective of this study was to find an accurate approximation technique (scheme) for solving linear differential equations. By exploiting the Trigonometric identity property of the Chebyshev polynomial, we developed a numerical scheme referred to … …Journal of Mathematics and Statistics, Vol. 5, Issue 2 · 30 Jun 2009 · 7,224 accessesView PDFCite
Research ArticleOpen accessEvery word in the titleNumerical Solution of Linear Integro-Differential EquationsHusein Jaradat, Omar Alsayyed, S. Al-SharaProblem Statement: Integro-differential equations find special applicability within scientific and mathematical disciplines. In this study, an analytical scheme for solving Integrodifferential equations was presented. Approach: We employed the Homotopy Analysis Method (HAM) to solve linear Fredholm integro-differential equations. Results: Error analysis and illustrative examples were included to demonstrate the validity and applicability of the technique. MATLAB 7 was used to … …Journal of Mathematics and Statistics, Vol. 4, Issue 4 · 31 Dec 2008 · 7,097 accessesView PDFCite
Research ArticleOpen accessEvery word in the titleBlock Methods based on Newton Interpolations for Solving Special Second Order Ordinary Differential Equations DirectlyYap Lee Ken, Fudziah Ismail, Mohamed Suleiman, Suriah Md. AminThis study focused mainly on the derivation of the 2 and 3-point block methods with constant coefficients for solving special second order ordinary differential equations directly based on Newton-Gregory backward interpolation formula. The performance of the new methods was compared with the conventional 1-point method using a standard set of test problems. Numerical results were presented to illustrate the effectiveness … …Journal of Mathematics and Statistics, Vol. 4, Issue 3 · 30 Sep 2008 · 8,126 accessesView PDFCite