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8 results for “Chebyshev polynomial”
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Research ArticleOpen accessIn the keywordsNumber of Spanning Trees of Circulant Graphs C6n and their ApplicationsS. N. DaoudProblem statement: The number of spanning trees of a graph G is usually denoted by τ(G). A circulant graph with n vertices and k jumps is Cn (a1,…..,ak). Approach: In this study the number τ(G) of spanning trees of the circulant graphs C6n with some non-fixed jumps such as C6n (1, n), C6n (1, n, 2n), C6n (1, n, 3n), … …Journal of Mathematics and Statistics, Vol. 8, Issue 1 · 12 Dec 2011 · 7,632 accessesView PDFCite
Research ArticleOpen accessIn the keywordsComplexity of Cocktail Party Graph and Crown GraphS. N. DaoudProblem statement: The number of spanning trees τ(G) in graphs (networks) was an important invariant. Approach: Using the properties of the Chebyshev polynomials of the second kind and the linear algebra techniques to evaluate the associated determinants. Results: The complexity, number of spanning trees, of the cocktail party graph on 2n vertices, given in detail in the text was proved. … …American Journal of Applied Sciences, Vol. 9, Issue 2 · 12 Dec 2011 · 7,872 accessesView PDFCite
Research ArticleOpen accessIn the keywordsHalf-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 · 7,277 accessesView PDFCite
Research ArticleOpen accessIn the keywordsA Note on the Numerical Solution for Fredholm Integral Equation of the Second Kind with Cauchy kernelM. Abdulkawi, M.M.A. Nik Long, Z. K. EshkuvatovProblem statement: In this study, numerical solution for the Fredholm integral equation of the second kind with Cauchy singular kernel is presented. Approach: The Chebyshev polynomials of the second kind are used to approximate the unknown function. Results: Numerical results are given to show the accuracy of the present numerical solution. Conclusion: The present numerical solution to the Fredholm integral … …Journal of Mathematics and Statistics, Vol. 7, Issue 1 · 25 Mar 2011 · 7,681 accessesView PDFCite
Research ArticleOpen accessIn the keywordsOn 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 accessIn the keywordsOn the General Solution of First-Kind Hypersingular Integral EquationsSuzan J. Obaiys, Z. Abbas, N. M.A. Nik Long et al.A new algorithm is presented to provide a general solution for a first type Hyper singular Integral Equation (HSIE). The singular integral has been converted into a regular form by cancelling the singularity and then transforming it into a system of algebraic equation based orthogonal poly- nomials. We applied the convergence method presented by (Obaiys, 2013) to conform the numerical … …American Journal of Engineering and Applied Sciences, Vol. 9, Issue 2 · 28 Jan 2016 · 8,703 accessesView PDFCite
Research ArticleOpen accessIn the keywordsNumerical Solution of Fourth Order Linear Ordinary Differential Equations by Cubic Spline Collocation Tau MethodO.A. Taiwo, O.M. OgunlaranProblem Statement: Many boundary value problems that arise in real life situations defy analytical solution; hence numerical techniques are desirable to find the solution of such equations. New numerical methods which are comparatively better than the existing ones in terms of efficiency, accuracy, stability, convergence and computational cost are always needed. Approach: In this study, we developed and applied three … …Journal of Mathematics and Statistics, Vol. 4, Issue 4 · 31 Dec 2008 · 6,987 accessesView PDFCite
Research ArticleOpen accessIn the abstractInterpolating Operators for MultiapproximationEman Samir BhayaProblem statement: There are no simple definitions of operators for best multiapproximation and best one sided multiapproximation which work for any measurable function in Lp for, p>0. This study investigated operators that are good for best multiapproximation and best one sided multiapproximation. Approach: We first introduced some direct results related to the approximation problem of continuous functions by Hermit-Fejer interpolation … …Journal of Mathematics and Statistics, Vol. 6, Issue 3 · 30 Sep 2010 · 7,659 accessesView PDFCite