AN IMPROVED ROOT LOCATION METHOD FOR FAST CONVERGENCE OF NON-LINEAR EQUATIONS

In this paper an improved root location method has been suggested for nonlinear equations f(x)=0. The proposed improved root location method is very much effective for solving nonlinear equations and several numerical examples associated with algebraic and transcendental functions are present in this paper to investigate the new method. Throughout the study we have proved that proposed method is cubically convergent.  All the results are executed on MATLAB 16 which has a machine precision of around . Key words: Newton’s method, Iterative method, third order convergent, Root finding methods

CLOSED NEWTON COTES QUADRATURE RULES WITH DERIATIVES

In this research paper, a new family of numerical integration of closed newton cotes is introduced which uses the mean of arithmetic and geometric means at derivative value for the Evaluation of Definite Integral. These quadrature methods are shown to be more efficient than the existing quadrature rules. The error terms are obtained by using the concept of precision. Finally, the accuracy of proposed method is verified with numerical examples and the results are compared with existing methods numerically and graphically. Keywords – Numerical Integration, Closed Newton-cotes formula, Definite integral, Arithmetic mean, Geometric mean, Numerical examples. DOI: 10.7176/MTM/9-5-06 Publication date: May 31st 201

A Convergent Scheme for Solving Initial Value Problems with Polynomial and Exponential Functions

This paper presents the development of a convergent numerical scheme for the solution of initial value problems of first order ordinary differential equations. The scheme has been derived via the combination of two functions namely, polynomial and exponential functions. The local truncation error , order of convergence, consistency and stability of the proposed scheme have been analyzed in the present study.  The Taylor’s series expansion has been used to derive the principal term of . The Dahlquist’s test equation is used to investigate the linear stability region. It is observed that the newly proposed scheme is fourth order convergent, consistent and conditionally stable with the region of linear stability. Three IVPs of different nature have been solved numerically to check the applicability of a new proposed scheme. The absolute error has been calculated at each mesh point of the integration interval. The numerical results show that the scheme is computationally effective, adequate and compares favorably with exact solutions. The aid of MATLAB version: 9.2.0.538062 (R2017a) has been used to carry out all numerical calculations. Keywords: Local truncation error, Absolute error, stability, consistency, convergence. MSC: 34A12, 45L05, 65L05, 65L20, 65L7

An Efficient Three Step Method For finding the Root Of Non-linear Equation with Accelerated convergence.

We have made an effort to design an accurate numerical strategy to be applied in the vast computing domain of numerical analysis. The purpose of this research is to develop a novel hybrid numerical method for solving a nonlinear equation, That is both quick and computationally cheap, given the demands of today's technological landscape. Sixth-order convergence is demonstrated by combining the classical Newton method, on which this method is largely based, with another two-step third-order iterative process. The effectiveness index for this novel approach is close to 1.4309, and it requires only five evaluations of the functions without a second derivative. The findings are compared to standard practice. The provided technique demonstrates higher performance in terms of computational efficiency, productivity, error estimation, and CPU times. Moreover, its accuracy and performance are tested using a variety of examples from the existing literature. Keywords: efficient scheme, nonlinear application, nonlinear functions, error estimation, computational cost

An Improved L-Stable Scheme for Initial Value Problems Under Variable Step-Size Approach

A non-linear explicit scheme has been studied for autonomous and non-autonomous initial value problems in ordinary differential equations (ODEs). This research proposed fifth order of convergence. The stability region of the scheme is also shown, as is the evolution of the scheme's associated local truncation error. A few numerical experiments showed that the scheme is fit for initial value problems with singular solutions, blowup the ODEs, singularly perturbed and stiff problems. MATLAB R2019a was used for the numerical computations and plotting of results produced by all methods. Keywords. Nonlinear method, local truncation error, L-Stability, Variable step-size, autonomous and non-autonomous

TO DEVELOP EFFICIENT SCHEME FOR SOLVING INITIAL VALUE PROBLEM IN ORDINARY DIFFERENTIAL EQUATION

In this paper, a new scheme of Runge-Kutta (RK) type has been developed while evaluating two slope functions per step and maintaining the third order accuracy of the scheme. Local truncation error is obtained with the help of principal term which is obtained via multi variable Taylor series. It has been shown that the convergence order of the scheme is three and its stability polynomial is also derived. Some numerical examples are taken in order to compare the developed scheme with other existing schemes. It is observed that the developed scheme is better than other selected existing schemes and this comparison has been performed on the basis of slope evaluations per integration step, error analysis and computer time consumed by the scheme under consideration. KEY WORDS: Initial value problems, Runge-Kutta Scheme, Autonomous and non-autonomous differential equations, Zero stability. DOI: 10.7176/MTM/9-8-06 Publication date: August 31st 201

Evaluation of Cotton Seeds as Environmentally Liable Source for Neutral Protease

Proteases are considered one of the most imperative groups of enzymes and are used in bioremediation processes, leather, detergents, pharmaceutical and the food industry. The foremost aim of this study was to extract, purify, and characterize the protease enzyme from cotton seeds. Purification of the neutral protease was achieved with ammonium sulphate, which gave the best results at 60% concentration with a specific activity of 51 units/mg protein and 1.52 purification fold with a percentage yield of 10.5%. The protease was active and stable at a wide range of pH from 4.0–10.0 with an optimum pH of 7.0. The highest activity of the purified enzyme was found at 20 °C. The enzyme was thermally stable and retained 25% of its activity at 50o C. The activity of cottonseeds protease Fraction-IV was enhanced by 20% with ZnCl2 and 15% with CoCl2 as enzyme samples were heated for 10 minutes. The Casein and peptone assays were also performed to check its catalytic activity. Furthermore, the maximum hydrolysis rate (Vmax) and apparent Michaelis–Menten constant (Km) values of the purified protease were 19 μmol/min and 0.08 mol/L, respectively, while activation energy was found to be 12.47 KJ/mol

Modified LCM’S Approximation Algorithm for Solving Transportation Problems

In this paper, Modified LCM’s Approximation Algorithm for Solving Transportation Problems has been developed in order to gain foremost fundamental capable solution of transportation issues where entity cut down the transportation expensive. The proposed algorithm is correlate with popular presenting methods corralling NWCM, LCM and improved algorithm and purposed algorithm found that yield to better results. Algorithm is quickest and effective. Few examples are tested by using modified algorithm is correlate with open literature. Key Words: Transportation problem, Initial Basic Feasible Solution, Optimal Solution DOI: 10.7176/JIEA/10-3-02 Publication date: April 30th 202

AN EFFECTIVE APPROACH OF FOUR-STEP METHOD FOR OPTIMAL SOLUTION OF TRANSPORTATION PROBLEM

Transportation problem (TP) in operation research is one of the most in use optimization technique to deal the problems that are related with transportation of goods from sources to destinations. Initial Basic Feasible Solution (IBFS) plays a vital role in TP which offers a way to obtain the optimal solution. The objective is to prevail the total transportation cost equivalent or nearer to optimal solution. In this paper, an effective approach of Four Step Method (FSM) for optimal solution of TP has been brought up in order to get optimal solution of TPs. In this method we construct the Maximum Column Table (MCT) and Maximum Row Table (MRT). Several problems has been solved using this method to get the optimal solution. The outcomes of proposed method are contrasted with results of North West Corner Method (NWCM), Least Cost Method (LCM) and Vogal’s Approximation Method (VAM). It is observed that the proposed method is not only achieving better results but also overcoming the limitation of VAM. Key Words: Transportation problem, Initial Basic Feasible Solution, Optimal solution, Linear programming proble

Soft switching modulation strategy based on bipolar (PSM) with improved efficiency in high-frequency link inverters

High Frequency-Link (HFL) Inverters have been employed to integrate renewable energy sources into utility grids and electric vehicles. The soft-switching range of High-Frequency Link Inverters (HFLI) is increased using auxiliary inductors and capacitors. The application of auxiliary components increases the conduction loss and the complexity of the circuit. The literature indicates that the existing soft-switching methods suffer from higher duty cycle loss, voltage spikes, and lower efficiency owing to the resonance between the parasitic capacitance of switches and the leakage inductance of the transformer. Therefore, it is imperative to develop a modulation strategy that can improve the efficiency of HFLI. In this context, the proposed study develops a cycloconverter-type High-Frequency Link Inverter (CHFLI) based on a Bipolar Phase Shift Modulation (BPSM) strategy without the use of auxiliary components. The proposed modulation strategy enables the semiconductor switches to operate under zero voltage switching. The full-bridge inverter and Full Bridge Active Clamper Circuit (FBAC) switches operate at the same gating signals with a constant duty cycle of 50%. The proposed topology uses built-in magnetizing inductance to achieve zero voltage switching and reduce the duty cycle loss. The leakage energy is recycled from the output filter inductor to the load side using the FBAC. The results indicate that the proposed modulation strategy achieves ZVS and simultaneously achieves an efficiency of 95%. The proposed modulation strategy is easy to implement and does not require complex circuitry