Some New and Sharp Inequalities of Composite Simpson’s Formula for Differentiable Functions with Applications
Abstract
:1. Introduction
2. Main Results
3. Numerical Tests
4. Conclusions
Author Contributions
Funding
Data Availability Statement
Acknowledgments
Conflicts of Interest
References
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n | Exact | Approximation | Error | Error Bound | |
---|---|---|---|---|---|
2 | −0.725661 | −0.725921 | 2.59667 × 10−4 | 0.0796703 | ∖ |
4 | −0.725661 | −0.725677 | 1.58658 × 10−5 | 0.0398352 | 4.03267 |
8 | −0.725661 | −0.725662 | 9.86074 × 10−7 | 0.0199176 | 4.00808 |
16 | −0.725661 | −0.725661 | 6.15437 × 10−8 | 0.00995879 | 4.00201 |
32 | −0.725661 | 0.725661 | 3.84514 × 10−9 | 0.00497939 | 4.0005 |
64 | −0.725661 | 0.725661 | 2.403 × 10−10 | 0.0024897 | 4.00013 |
128 | −0.725661 | 0.725661 | 1.50183 × 10−11 | 0.00124485 | 4.00004 |
n | Exact | Approximation | Error | Error Bound | |
---|---|---|---|---|---|
2 | 1.08877 | 1.08877 | 5.12 × 10−4 | 0.268978 | ∖ |
4 | 1.08877 | 1.08829 | 3.2 × 10−5 | 0.134489 | 4.000 |
8 | 1.08877 | 1.08826 | 2 × 10−6 | 0.0672444 | 4.000 |
16 | 1.08877 | 1.08826 | 1.25 × 10−7 | 0.0336222 | 4.000 |
32 | 1.08877 | 1.08826 | 7.8125 × 10−9 | 0.0168111 | 4.000 |
64 | 1.08877 | 1.08826 | 4.88281 × 10−10 | 0.00840556 | 4.000 |
128 | 1.08877 | 1.08826 | 3.05174 × 10−11 | 0.00420278 | 4.0001 |
n | Exact | Approximation | Error | Error Bound | |
---|---|---|---|---|---|
2 | −0.725661 | −0.725921 | 2.59667 × 10−4 | 0.110118 | ∖ |
4 | −0.725661 | −0.725677 | 1.58658 × 10−5 | 0.0543655 | 4.03267 |
8 | −0.725661 | −0.725662 | 9.86074 × 10−7 | 0.0270543 | 4.00808 |
16 | −0.725661 | −0.725661 | 6.15437 × 10−8 | 0.0135057 | 4.00201 |
32 | −0.725661 | 0.725661 | 3.84514 × 10−9 | 0.00674964 | 4.0005 |
64 | −0.725661 | 0.725661 | 2.403 × 10−10 | 0.00337438 | 4.00013 |
128 | −0.725661 | 0.725661 | 1.50183 × 10−11 | 0.00168713 | 4.00004 |
n | Exact | Approximation | Error | Error Bound | |
---|---|---|---|---|---|
2 | 1.08877 | 1.08877 | 5.12 × 10−4 | 0.363368 | ∖ |
4 | 1.08877 | 1.08829 | 3.2 × 10−5 | 0.179557 | 4.000 |
8 | 1.08877 | 1.08826 | 2 × 10−6 | 0.0893993 | 4.000 |
16 | 1.08877 | 1.08826 | 1.25 × 10−7 | 0.0446394 | 4.000 |
32 | 1.08877 | 1.08826 | 7.8125 × 10−9 | 0.0223111 | 4.000 |
64 | 1.08877 | 1.08826 | 4.88281 × 10−10 | 0.0111544 | 4.000 |
128 | 1.08877 | 1.08826 | 3.05174 × 10−11 | 0.00557706 | 4.0001 |
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Liu, W.; Wang, Y.; Sial, I.B.; Ciurdariu, L. Some New and Sharp Inequalities of Composite Simpson’s Formula for Differentiable Functions with Applications. Mathematics 2025, 13, 1814. https://doi.org/10.3390/math13111814
Liu W, Wang Y, Sial IB, Ciurdariu L. Some New and Sharp Inequalities of Composite Simpson’s Formula for Differentiable Functions with Applications. Mathematics. 2025; 13(11):1814. https://doi.org/10.3390/math13111814
Chicago/Turabian StyleLiu, Wei, Yu Wang, Ifra Bashir Sial, and Loredana Ciurdariu. 2025. "Some New and Sharp Inequalities of Composite Simpson’s Formula for Differentiable Functions with Applications" Mathematics 13, no. 11: 1814. https://doi.org/10.3390/math13111814
APA StyleLiu, W., Wang, Y., Sial, I. B., & Ciurdariu, L. (2025). Some New and Sharp Inequalities of Composite Simpson’s Formula for Differentiable Functions with Applications. Mathematics, 13(11), 1814. https://doi.org/10.3390/math13111814