Numerical Double Integration for Unequal Data Spaces
Автор: Md. Nayan Dhali, Nandita Barman, Md. Mohedul Hasan, A. K. M. Selim Reza
Журнал: International Journal of Mathematical Sciences and Computing @ijmsc
Статья в выпуске: 6 vol.6, 2020 года.
Бесплатный доступ
Numerical integral is one of the mathematical branches that connect between analytical mathematics and computer. Numerical integration is a primary tool used by engineers and scientists to obtain an approximate result for definite integrals that cannot be solved analytically. Numerical double integration is widely used in calculating surface area, the intrinsic limitations of flat surfaces and finding the volume under the surface. A wide range of method is applied to solve numerical double integration for equal data space but the difficulty is arisen when the data values are not equal. In this paper we have tried to generate a mathematical formula of numerical double integration for unequal data spaces. Trapezoidal rule for unequal space is used to evaluate the formula. We also verified our proposed model by demonstrating some numerical examples and compared the numerical result with the analytical result.
Numerical Integral, Numerical Double Integration, Newton`s Divided Difference, Trapezoidal Rule
Короткий адрес: https://sciup.org/15017569
IDR: 15017569 | DOI: 10.5815/ijmsc.2020.06.04
Список литературы Numerical Double Integration for Unequal Data Spaces
- M. Buchibrand, 7 forms of divorce in Africa, Retrieved on 22nd May 2018 from https://www.nairaland.com/2526539/7-forms-divorce-africa, 2016. [1] Al-Jarrah, R. On the Lagrange Interpolation Polynomials. Journal of Approximation Theory 41, 170-l 78, 1884.
- Anton, H., Bivens, I., & Davis, S. Calculas Early Transcendentals. United States of America: John Wiley & Sons, Inc, 2012.
- Das, B., & Chakrabarty, D. Lagrange’s Interpolation Formula: Representation of Numerical Data by a Polynomial curve. International Journal of Mathematics Trends and Technology (IJMTT), 3, 2016.
- Dahiya, V. Analysis of Lagrange Interpolation Formula. IJISET - International Journal of Innovative Science, Engineering & Technology, 1(10), 2014.
- Darkwah, K. A., Norttey, E. N. N., & Anan, C. A Proposed Numerical Integration Method Using Polynomial Interpolation. British Journal of Mathematics & Computer Science, 16, 1-10, 2016.
- Dhali, M. N., Bulbul, M. F., & Sadiya, U. Comparison on Trapezoidal and Simpson's Rule for Unequal Data Space. International Journal of Mathematical Sciences and Computing, 5(4), 33-43, DOI: 10.5815/ijmsc.2019.04.04, 2019.
- Douglas, F. J., & Burden, L. R. Numerical Analysis, Thomson Learning, 2001.
- Gill, P. E., & Miller, G. F. An algorithm for the integration of unequally spaced data. Computer Journal, 15, 80-83, 1972.
- Hildebrand, F. B. & Graw-Hill, M. Introduction to Numerical Analysis. New Work, 1974.
- Jayakumar, J. Generalized Simpson-Newton's Method for Solvinf Nonlinear Equations with Cubic Convergence. IQSR Journal of Mathematics, 7(5), 58-61, 2013.
- Khan, M.-U.-R., Hossain, M., & Parvin, S. Numerical Integration Schemes for Unequal Data Spacing. American Journal of Applied Mathematics, 5(2), 48-56, 2017.
- Muthumalai, R. K. Some Formulas For Numerical Differentiation Through Divided Differences. International Journal of Mathematical Archive(3), 2012.
- Muosa, S. M. Numerical Methods for Evaluation of Double integrals with Continuous Integrands, International Journal of Pure and Applied Mathematics, Volume 119, No. 10, 385-396, 2018.
- Saputra, A., Bakri, R. and Mahmud, R. Numerical Analysis of Double Integral of Trigonometric Function Using Romberg Method. Daya Matematis: Jurnal Inovasi Pendidikan Matematika, Vol. 2, No. 2, 131-136, 2020.
- Sinha, R K and Kumar, R. Numerical method for evaluating the integrable function on a finite interval. International Journal of Engineering Science and Technology. 2(6), 2010.
- Sozio, G. Numerical Integration. Australian Senior Mathematics Journal. 23(1), 2009.
- Thukral, R. Further Acceleration of the Simpson’s Method for Solving Non-linear Equation. Journal of Advances in Mathematics, 14, 02, 2018.
