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# Browsing SWL-Mathematics and Natural Sciences by Author "Muhammad, Imran"

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• (2017-11-14)
We discussed some derivations of Simpson rule formulas that are not commonly discussed in numerical analysis texts. The derivation involved a Lagrange interpolating polynomial, and a quadratic polynomial analytically and ...
• (2017-11-14)
We modify a new iterative method introduced by Abu-Alshaikh [Enformatika. 5 (2005) h. 190--193] to speed up the convergence for finding multiple roots of a nonlinear equation in one variable. Comparison between the discussed ...
• (2016-04-22)
This article discusses about application of linear quadratic regulator in linear model of Love and Happiness with Affair. This paper focus on model with condition that make its unstable. Optimal control is used to control ...
• (2017-11-14)
In this paper we propose a new modification of Newton's method based on midpoint rule for solving nonlinear equations. Analysis of convergence shows that the new method is cubically convergent for a simple root and linearly ...
• (2017-11-14)
We discuss modified Newton’s method using heronian mean instead of arithmetic mean. We show that this modification is of order three for a simple root. Comparisons among mean based Newton’s method are given by considering ...
• (2017-11-14)
A modified regulafalsi method, for solving a nonlinear equation of a single variable,based on applying another linear interpolation as corrector without any addition of function evaluations is presented in this paper. The ...
• (2017-09-14)
In this paper we discuss a new modification of Newton’s method based on Root Mean Square rule for solving nonlinear equations. We show that the convergence of the proposed method is of order three. We verify the theoretical ...
• (2017-11-14)
We discuss and do some analysis on numerical integration based on interpolation, midpoint, trapezoidal rule and Simpson rule. We end up with some new formulas, which are not mentioned in numerical analysis textbooks. The ...
• (2017-11-14)
We discuss modified Newton methods, by looking at an approximation errorof a numerical approximation on an integral, and propose a modification usingmidpoint rule. Comparison among the discussed methods is also given ...