Further Acceleration of the Simpson Method for Solving Nonlinear Equations

There are two aims of this paper, firstly, we present an improvement of the classical Simpson third-order method for finding zeros a nonlinear equation and secondly, we introduce a new formula for approximating second-order derivative. The new Simpson-type method is shown to converge of the order four.  Per iteration the new method requires same amount of evaluations of the function and therefore the new method has an efficiency index better than the classical Simpson method.  We examine the effectiveness of the new fourth-order Simpson-type method by approximating the simple root of a given nonlinear equation. Numerical comparisons is made with classical Simpson method to show the performance of the presented method

Another Newton-type method with (k+2) order convergence for solving quadratic equations

In this paper we define another Newton-type method for finding simple root of quadratic equations. It is proved that the new one-point method has the convergence order of k  2 requiring only three function evaluations per full iteration,where k is the number of terms in the generating series. The Kung and Traub conjecture states that the multipoint iteration methods, without memory based on n function evaluations, could achieve maximum convergence order 1 2nï€ ­but, the new method produces convergence order of nine, which is better than the expected maximum convergence order. Finally, we have demonstrated that our present method is very competitive with the similar methods

IDENTIFICATION OF AMPC Î’-LACTAMASE-PRODUCING CLINICAL ISOLATES OF ESCHERICHIA COLI

  Objective: Indiscriminate use of β-lactam antibiotics has resulted in the emergence of β-lactamase enzymes. AmpC β-lactamases, in particular, confer resistance to penicillin, first-, second-, and third-generation cephalosporins as well as monobactams and are responsible for antibiotic resistance in nosocomial pathogens. Therefore, this study was undertaken to screen nosocomial Escherichia coli isolates for the presence and characterization of AmpC β-lactamases. The study also envisaged on the detection of inducible AmpC β-lactamases and extended-spectrum β-lactamases (ESBLs) in AmpC β-lactamase-producing E. coli.Methods: A total of 102 clinical isolates of E. coli, were subjected to cefoxitin screening, and screen-positive isolates were further subjected to inhibitor-based detection method, phenotypic confirmatory test, disc antagonism test, polymerase chain reaction (PCR), and isoelectric focusing (IEF).Results: In this study, 33% of E. coli were resistant to cefoxitin, of which 35% were found to be positive for AmpC β-lactamase by inhibitor-based phenotypic test. Of the AmpC-positive isolates, 83% were positive for ESBLs, whereas 25% were producing inducible AmpC β-lactamases. PCR and IEF showed CIT and EBC types of AmpC β-lactamases present in the tested isolates.Conclusion: Our study showed the presence of inducible AmpC enzymes and ESBLs in E. coli isolates and PCR identified more isolates to be AmpC producers

Modified Newton method to determine multiple zeros of nonlinear equations

New one-point iterative method for solving nonlinear equations is constructed.  It is proved that the new method has the convergence order of three. Per iteration the new method requires two evaluations of the function.  Kung and Traub conjectured that the multipoint iteration methods, without memory based on n evaluations, could achieve maximum convergence order2n-1  but, the new method produces convergence order of three, which is better than expected maximum convergence order of two.  Hence, we demonstrate that the conjecture fails for a particular set of nonlinear equations. Numerical comparisons are included to demonstrate exceptional convergence speed of the proposed method using only a few function evaluations

New variants of the Schroder method for finding zeros of nonlinear equations having unknown multiplicity

There are two aims of this paper, firstly, we define new variants of the Schroder method for finding zeros of nonlinear equations having unknown multiplicity and secondly, we introduce a new formula for approximating multiplicity m. Using the new formula, the five particular well-established methods are identical to the classical Schroder method. In terms of computational cost the new iterative method requires three evaluations of functions per iteration. It is proved that the each of the methods has a convergence of order two. Numerical examples are given to demonstrate the performance of the methods with and without multiplicity m

Introduction to a family of Thukral k-order method for finding multiple zeros of nonlinear equations

A new one-point k-order iterative method for finding zeros of nonlinear equations having unknown multiplicity is introduced.  In terms of computational cost the new iterative method requires k+1 evaluations of functions per iteration.  It is shown that the new iterative method has a convergence of order k