scholarly journals Improving the Accuracy of the Trapezoidal Rule

SIAM Review ◽  
2021 ◽  
Vol 63 (1) ◽  
pp. 167-180
Author(s):  
Bengt Fornberg
Keyword(s):  
Trapezoidal Rule

scholarly journals New Approximation Methods Based on Fuzzy Transform for Solving SODEs: II

2018 ◽  
Vol 1 (3) ◽  
pp. 30 ◽  
Author(s):  
Hussein ALKasasbeh ◽  
Irina Perfilieva ◽  
Muhammad Ahmad ◽  
Zainor Yahya
Keyword(s):  
Numerical Methods ◽  
Differential Equations ◽  
Trapezoidal Rule ◽  
Approximation Methods ◽  
System Of Differential Equations ◽  
Fuzzy Transform ◽  
Fuzzy Partition ◽  
Fuzzy Approximation ◽  
One Step ◽  
Basic Functions

In this research, three approximation methods are used in the new generalized uniform fuzzy partition to solve the system of differential equations (SODEs) based on fuzzy transform (FzT). New representations of basic functions are proposed based on the new types of a uniform fuzzy partition and a subnormal generating function. The main properties of a new uniform fuzzy partition are examined. Further, the simpler form of the fuzzy transform is given alongside some of its fundamental results. New theorems and lemmas are proved. In accordance with the three conventional numerical methods: Trapezoidal rule (one step) and Adams Moulton method (two and three step modifications), new iterative methods (NIM) based on the fuzzy transform are proposed. These new fuzzy approximation methods yield more accurate results in comparison with the above-mentioned conventional methods.

scholarly journals An improved Trapezoidal rule for numerical integration

2021 ◽  
Vol 2090 (1) ◽  
pp. 012104
Author(s):  
A. F Abdulhameed ◽  
Q A Memon
Keyword(s):  
Numerical Integration ◽  
Integration Method ◽  
Research Community ◽  
Trapezoidal Rule ◽  
Engineering Software ◽  
Engineering Problems ◽  
Current Century ◽  
Single Interval ◽  
Improved Accuracy ◽  
Higher Order Functions

Abstract Numerical Methods have attracted of research community for solving engineering problems. This interest is due to its practicality and the improvement of highspeed calculations done on current century processors. The increase in numerical method tools in engineering software, such as Matlab, is an example of the increased interest. In this paper, we are present a new improved numerical integration method, that is based on the well-known trapezoidal rule. The proposed method gives a great enhancement to the trapezoidal rule and overcomes the issue of the error value when dealing with some higher order functions even when solving for a single interval. After literature review, the proposed system is mathematically explained along with error analysis. Few examples are illustrated to prove improved accuracy of the proposed method over traditional trapezoidal method.

scholarly journals Improving the two-stage numerical integration in stability identification of oscillation with distributed delay

2019 ◽  
Vol 11 (1) ◽  
pp. 168781401881990
Author(s):  
Chigbogu Godwin Ozoegwu
Keyword(s):  
Numerical Integration ◽  
Distributed Delay ◽  
Original Method ◽  
Higher Order ◽  
Trapezoidal Rule ◽  
Point Of View ◽  
Engineering Systems ◽  
Two Stage ◽  
Integration Rule ◽  
Integration Rules

The vibration of the engineering systems with distributed delay is governed by delay integro-differential equations. Two-stage numerical integration approach was recently proposed for stability identification of such oscillators. This work improves the approach by handling the distributed delay—that is, the first-stage numerical integration—with tensor-based higher order numerical integration rules. The second-stage numerical integration of the arising methods remains the trapezoidal rule as in the original method. It is shown that local discretization error is of order [Formula: see text] irrespective of the order of the numerical integration rule used to handle the distributed delay. But [Formula: see text] is less weighted when higher order numerical integration rules are used to handle the distributed delay, suggesting higher accuracy. Results from theoretical error analyses, various numerical rate of convergence analyses, and stability computations were combined to conclude that—from application point of view—it is not necessary to increase the first-stage numerical integration rule beyond the first order (trapezoidal rule) though the best results are expected at the second order (Simpson’s 1/3 rule).

On Simplex Trapezoidal Rule Families

1980 ◽  
Vol 17 (1) ◽  
pp. 126-147 ◽  
Author(s):  
J. N. Lyness ◽  
A. C. Genz
Keyword(s):  
Trapezoidal Rule
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