Approximating the area of a tabulated data with equally spaced interval using Newton-Cotes Quadrature formulas / Mayleen Virginia I. Tolidanes
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TextLanguage: English Publication details: 2003Description: 33 leavesSubject(s): Dissertation note: Thesis (BS Applied Mathematics) -- University of the Philippines Mindanao, 2003 Abstract: This paper presents a simple and widely applicable numerical approach on approximating the area of a tabulated data with equally spaced interval using Newton-Cotes quadrature formulas. The closed form Newton-Cotes formulas used in this study include; Trapezoidal Rule, Simpson's 1/3 Rule, Simpson's 3/8 Rule and Boole's Rule. The primary goal of the study was to investigate and determine which quadrature formula works best over the six representative test functions. Trapezoidal Rule performed well but has slow convergence. Simson's 3/8 gave good results with small values of n but was surpassed by the Simpson's 1/3 which, performed better as the subintervals increase. On the other hand, Boole's Rule has slow convergence for small n?s and fast convergence for large values of n. the numerical experiment showed that Simpson's 1/3 Rule performs best because it gave the least errors for all six test functions.
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University Library Theses | Room-Use Only | LG993.5 2003 A64 T65 (Browse shelf(Opens below)) | Not For Loan | 3UPML00010402 | |
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University Library Archives and Records | Preservation Copy | LG993.5 2003 A64 T65 (Browse shelf(Opens below)) | Not For Loan | 3UPML00020891 |
Thesis (BS Applied Mathematics) -- University of the Philippines Mindanao, 2003
This paper presents a simple and widely applicable numerical approach on approximating the area of a tabulated data with equally spaced interval using Newton-Cotes quadrature formulas. The closed form Newton-Cotes formulas used in this study include; Trapezoidal Rule, Simpson's 1/3 Rule, Simpson's 3/8 Rule and Boole's Rule. The primary goal of the study was to investigate and determine which quadrature formula works best over the six representative test functions. Trapezoidal Rule performed well but has slow convergence. Simson's 3/8 gave good results with small values of n but was surpassed by the Simpson's 1/3 which, performed better as the subintervals increase. On the other hand, Boole's Rule has slow convergence for small n?s and fast convergence for large values of n. the numerical experiment showed that Simpson's 1/3 Rule performs best because it gave the least errors for all six test functions.
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