Some weighted quadrature methods based upon the mean value theorems
Copyright policy )Some weighted quadrature methods based upon the mean value theorems
In this paper, a class of weighted quadrature methods is introduced for smooth functions based upon the use of the mean value theorems. These new quadrature rules are also treated in a systematic approach involving formal series expansion. The convergence analysis of the proposed method is studied here for both the non‐weighted and the weighted cases. Some potential areas and directions for extensions and applications of the results, which are presented in this paper, are also indicated.
- University of Victoria Canada
- University of Regensburg Germany
- Azerbaijan University Azerbaijan
- K.N.Toosi University of Technology Iran (Islamic Republic of)
- Azerbaijan University of Languages Azerbaijan
series expansions, weight functions, Bernoulli, Differentiation (real functions of one variable): general theory, generalized derivatives, mean value theorems, Series expansions (e.g., Taylor, Lidstone series, but not Fourier series), weighted and non-weighted cases, Approximate quadratures, convergence analysis, interpolatory quadrature formulas, Euler, and Genocchi polynomials, mean value theorems, Newton-Cotes formula, Numerical integration, quadrature rules, ordinary differential equations (ODEs), Lagrange polynomial interpolant
series expansions, weight functions, Bernoulli, Differentiation (real functions of one variable): general theory, generalized derivatives, mean value theorems, Series expansions (e.g., Taylor, Lidstone series, but not Fourier series), weighted and non-weighted cases, Approximate quadratures, convergence analysis, interpolatory quadrature formulas, Euler, and Genocchi polynomials, mean value theorems, Newton-Cotes formula, Numerical integration, quadrature rules, ordinary differential equations (ODEs), Lagrange polynomial interpolant
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