[PDF] Top 20 Approximation of the Stieltjes Integral and Applications in Numerical Integration

... the Stieltjes integral and applications in nu- merical integration are ...The Stieltjes integral is approximated by the product of the divided difference of the integrator and ... See full document

... The following corollary which provides an upper bound for the approximation error in the trapezoid quadrature formula, for f of bounded variation, holds [4]. Corollary 2. Assume that f : [a, b] → R is of bounded ... See full document

... We now derive various sophisticated bounds for some differences and prod- ucts of the above special means using the results obtained in the previous section. These bounds are useful in applications since the ... See full document

... DRAGOMIR, On the Ostrowski’s integral inequality for mappings with bounded variation and applications, Mathematical Inequalities and Applications, 4(1) (2001), 59-66.. [6] S.S.[r] ... See full document

... Abstract. Sharp error estimates in approximating the Riemann-Stieltjes in- tegral with (l, L)-Lipschitzian integrators and applications for the ˇ Cebyˇ sev functional are given. Some inequalities that ... See full document

... a numerical framework for solving partial differential ...the numerical tools used for accomplishing the required ...for integration over one-dimensional and two-dimensional ...for ... See full document

... Dragomir, A generalization of Ostrowski’s integral inequality for mappings with bounded variation and applications in numerical integration, Bull.. Soc ., accepted.[r] ... See full document

... S.S. DRAGOMIR AND N.S. An integral inequality of Ostrowski’s type for mappings whose second derivatives are bounded is proved. Applications in Numerical Integration and for special means[r] ... See full document

... WANG, An inequality of Ostrowski-Gr¨ uss’ type and its applications to the estimation of error bounds for some special means and for some numerical quadrature rules, Computers Math. WANG[r] ... See full document

... 1. Introduction. Adomian polynomial algorithm has been extensively used to solve linear and nonlinear problems arising in many interesting applications (see, e.g., [1, 2, 4, 5]). The algorithm (a decomposition ... See full document

... its integral mean. It has wide applications in Numerical integration and Probability ...for numerical quadrature ...to Numerical quadrature rules and Probability ... See full document

... (1.1). Applications for three point quadrature rules of functions that are (n 1) di¤erentiable (n 1) with the derivative f (n 1) absolutely continuous are given as ... See full document

... in the case when the integrand f is continuous while the function of bounded variation g is S-dominated by a pair of monotonic functions in the sense presented at the beginning of the next section. The ... See full document

... Assume that u; f : [a; b] ! C . If the Riemann-Stieltjes integral R a b f (t) du (t) exists, we write for simplicity, like in [1, p. 142] that f 2 R C (u; [a; b]) ; or R C (u) when the interval is ... See full document

... 2 M. Domingo Montesinos, A. I. Garralda Guillem, and M. Ruiz Gal´an, “Fredholm integral equations and Schauder bases,” in VIII Journ´ees Zaragoza-Pau de Math´ematiques Appliqu´ees et de Statistiques, vol. 31 of ... See full document

... DRAGOMIR, A generalization of Gr¨ uss’ inequality in inner product spaces and appli- cations, J.. FEDOTOV, An inequality of Gr¨ uss’ type for Riemann-Stieltjes integral and applications [r] ... See full document

... FEDOTOV, An inequality of Gr¨ uss type for the Riemann-Stieltjes integral and applications for special means, Tamkang J. FEDOTOV, A Gr¨ uss type inequality for mappings of bounded[r] ... See full document

... Stieltjes integral, Functions of bounded variation, Lipschitzian func- tions, Monotonic functions, Quadrature rules.. 1..[r] ... See full document

... Riemann-Stieltjes integral BVPs (boundary value problems) is considered. By applying shooting method and comparison principle, we obtain some new results which extend the known ones. At the same time, the ... See full document

... 3 Numerical Schemes 47 4.4 Convergence Results 53 4.5 Asymptotic Expansions and Numerical Stability 60 4.6 Numerical Example 68 4.7 An Alternative Formulation 68 The Numerical Solution o[r] ... See full document