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Research ArticleOpen accessEvery word in the titleHalf-bounded Numerical Solution of Singular Integral Equations with Cauchy KernelM. Abdulkawi, Z. K. Eshkuvatov, N.M.A. Nik LongProblem statement: In this study, a numerical solution for singular integral equations of the first kind with Cauchy kernel over the finite segment [-1,1] is presented. The numerical solution is bounded at x =1 and unbounded at x = -1. Approach: The numerical solution is derived by approximating the unknown density function using the weighted Chebyshev polynomials of the fourth … …Journal of Mathematics and Statistics, Vol. 7, Issue 1 · 25 Mar 2011 · 7,269 accessesView PDFCite
Research ArticleOpen accessEvery word in the titleVariational Homotopy Perturbation Method for the Zakharove-Kuznetsov EquationsMashaallah Matinfar, Maryam GhasemiProblem statement: In this research, the Variational Homotopy Perturbation Method (VHPM) which is a combination of Variational Iteration Method (VIM) and Homotopy Perturbation Method (HPM) used for the Zakharove-Kuznetsov equations (ZK-equations). Approach: These two methods are proposed by chinese researcher J.H.He. M.A.Noor improved these two methods and established the VHPM. The numerical solution of ZK-equation is of great importance dut … …Journal of Mathematics and Statistics, Vol. 6, Issue 4 · 24 Dec 2010 · 7,254 accessesView PDFCite
Research ArticleOpen accessEvery word in the titleUsing Regression to Establish Weights for a Set of Composite Equations through a Numerical Analysis Approach: A Case of Admission Criteria to a CollegeRamzi Naim Nasser, Viviane NaimyProblem statement: Mathematically little is known of college admission criteria as in school grade point average, admission test scores or rank in class and weighting of the criteria into a composite equation. Approach: This study presented a method to obtain weights on “composite admission” equation. The method uses an iterative procedure to build a prediction equation for an optimal weighted … …Journal of Mathematics and Statistics, Vol. 6, Issue 3 · 30 Sep 2010 · 7,179 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 · 8,538 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 · 6,598 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 · 6,873 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 · 7,222 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 · 7,093 accessesView PDFCite
Research ArticleOpen accessEvery word in the titleAnalytical Investigation of Hyperbolic Equations via He's MethodsD.D. Ganji, M. Amini, A. KolahdoozPerturbation methods depend on a small parameter which is difficult to be found for real-life nonlinear problems. To overcome this shortcoming, two new but powerful analytical methods were introduced to solve nonlinear heat transfer problems in this Letter, one is He's Variational Iteration Method (VIM) and the other is the Homotopy-Perturbation Method (HPM). Nonlinear hyperbolic equations were used as examples … …American Journal of Engineering and Applied Sciences, Vol. 1, Issue 4 · 31 Dec 2008 · 7,115 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 · 8,120 accessesView PDFCite