Sinc Based Method For The Approximation Of Indefinite Integral Fedpuka Journal of Science, Technology & Contemporary Studies, Vol.. 2 No. 2.
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Abstract
A variable transformation function incorporated with the sinc procedure was employed in the numerical approximation of indefinite integrals that are analytic in (0, s). The modified error function used for this process proved to be efficient for the computation and showed an improved convergence of order CN1/3exp(-N2/3) thus converging faster when compared to results obtained using the numerical procedure based on the modified tanh function as number of evaluation N increases. Numerical examples are given in this work to demonstrate the procedure.
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References
Haber. S. (1977). The tanh rule for numerical integration, Siam Journal of Numerical analysis 14(4): 668-685.
John, E. D. & Ogbonna, N. (2016). A double exponential Sinc collocation method for Volterra-Fredholm integral equations of the second kind, Journal of Nigerian Mathematical Society, 35 (3): 408-423.
Kearfott. R. B. (1983). A Sinc approximation for the indefinite integral, Mathematics of Computation, 41(164): 559-572.
McNamee, J., Stenger & Whitney,F. L. (1971). Whittaker’s cardinal function in retrospect, Mathematics of Computation, 25(113): 141-154
Mei Yang & Fengqun Zhao (2021). Sinc numerical methods for time nonlocal parabolic equations, J. Phys.: Conf. Ser. 1903 012053
Muhammad M & Mori, M. (2003). Double exponential formulas for numerical indefinite integration, Journal of Computational and Applied Mathematics 161: 431-448.
Okayama, T., Matsuo, T. & Sugihara, M. (2013)., Error estimate with explicit constants for Sinc approximation, Sinc quadrature and Sinc indefinite integration, Numerische Mathematik, 124(2): 361-394.
Stenger, F. (1993). Numerical methods based on Sinc and analytic functions, Springer Verlag, 565 pages
Sugihara, M. (1997). Optimality of double exponential formulas - functional analysis approach, Numerische Mathematik, 75: 379-395.
e, L. (2006). Numerical quadrature: Theory and Computation, M.Sc. Thesis, Dalhousie University, Halifax, Nova Scotia, 90 pages.