A novel Romberg integration method for neutrosophic valued functions

Decision Analytics Journal - Tập 9 - Trang 100338 - 2023
Suvankar Biswas1, Smita Pal Sarkar2, Sandip Moi3
1Discipline of Mathematics, School of Sciences, Indira Gandhi National Open University, New Delhi 110068, India
2Department of Mathematics, Indian Institute of Engineering Science and Technology, Shibpur, B. Garden, Howrah 711103, India
3Department of Mathematics, Indian Institute of Engineering Science and Technology, Shibpur, B. Garden, Howrah, 711103, India

Tóm tắt

This study proposes a numerical integration technique to determine the approximate integral of the neutrosophic valued function. Newton Cot’s method with a positive coefficient has been used for neutrosophic integration, and then the suggested technique is used to find the approximate value of the integral. This method is called the Romberg integration method. In this method, the composite trapezoidal rule is applied initially, and Richardson’s extrapolation technique is used next to improve the solution. Richardson’s extrapolation is the basis of Romberg’s integration. Formulas with high-order truncation errors are created using Richardson extrapolation, which employs an averaging method. Richardson’s extrapolation helps the proposed method to achieve high computational efficiency. The convergence of the numerical approximation is provided in terms of theorems. A comparative analysis of the proposed method with other existing methods is demonstrated to show the efficiency and reliability of the proposed method.

Từ khóa

#Neutrosophic integration #Newton Cot’s formula #Peano’s error representation #Romberg integration #Richardson extrapolation

Tài liệu tham khảo

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