SINDH UNIVERSITY RESEARCH JOURNAL (SCIENCE SERIES), 2019
In this paper, a new modified algorithm is derived for combined numerical integration. Numerical ... more In this paper, a new modified algorithm is derived for combined numerical integration. Numerical integration is used to evaluate definite integral which cannot be evaluated analytically. In order to obtain higher order accuracy in the solution, mostly higher order quadrature rules are used which also introduces rounding off errors. In order to mitigate such errors, it has been proposed to use a combination of lower order rules to improve the accuracy and reduce error. Several definite integrals have been approximated and the results have been compared with the existing rules and a rule proposed by (Md.Amanat Ullah, 2015). The rules from the closed quadrature family, namely, Weddle's rule, Boole's rule, Simpson's rule and Trapezoidal rule have also been used. It has been found that the new proposed modified algorithm attains improved order of accuracy in comparison of the existing rules and the rule of Md.Amanat Ullah for a fixed number of subintervals.
In this paper, a new modified algorithm is derived for combined numerical integration. Numerical ... more In this paper, a new modified algorithm is derived for combined numerical integration. Numerical integration is used to evaluate definite integral which cannot be evaluated analytically. In order to obtain higher order accuracy in the solution, mostly higher order quadrature rules are used which also introduces rounding off errors. In order to mitigate such errors, it has been proposed to use a combination of lower order rules to improve the accuracy and reduce error. Several definite integrals have been approximated and the results have been compared with the existing rules and a rule proposed by (Md.Amanat Ullah, 2015). The rules from the closed quadrature family, namely, Weddle's rule, Boole's rule, Simpson's rule and Trapezoidal rule have also been used. It has been found that the new proposed modified algorithm attains improved order of accuracy in comparison of the existing rules and the rule of Md.Amanat Ullah for a fixed number of subintervals.
SINDH UNIVERSITY RESEARCH JOURNAL (SCIENCE SERIES), 2019
In this paper, a new modified algorithm is derived for combined numerical integration. Numerical ... more In this paper, a new modified algorithm is derived for combined numerical integration. Numerical integration is used to evaluate definite integral which cannot be evaluated analytically. In order to obtain higher order accuracy in the solution, mostly higher order quadrature rules are used which also introduces rounding off errors. In order to mitigate such errors, it has been proposed to use a combination of lower order rules to improve the accuracy and reduce error. Several definite integrals have been approximated and the results have been compared with the existing rules and a rule proposed by (Md.Amanat Ullah, 2015). The rules from the closed quadrature family, namely, Weddle's rule, Boole's rule, Simpson's rule and Trapezoidal rule have also been used. It has been found that the new proposed modified algorithm attains improved order of accuracy in comparison of the existing rules and the rule of Md.Amanat Ullah for a fixed number of subintervals.
In this paper, a new modified algorithm is derived for combined numerical integration. Numerical ... more In this paper, a new modified algorithm is derived for combined numerical integration. Numerical integration is used to evaluate definite integral which cannot be evaluated analytically. In order to obtain higher order accuracy in the solution, mostly higher order quadrature rules are used which also introduces rounding off errors. In order to mitigate such errors, it has been proposed to use a combination of lower order rules to improve the accuracy and reduce error. Several definite integrals have been approximated and the results have been compared with the existing rules and a rule proposed by (Md.Amanat Ullah, 2015). The rules from the closed quadrature family, namely, Weddle's rule, Boole's rule, Simpson's rule and Trapezoidal rule have also been used. It has been found that the new proposed modified algorithm attains improved order of accuracy in comparison of the existing rules and the rule of Md.Amanat Ullah for a fixed number of subintervals.
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