VOLUME 10, ISSUE 11, NOVEMBER 2022

Abstract: In this paper, we have given provided all the information “Newton’s forward and backward interpolation method”, as this method is used for equal intervals, and both forward and backward is applied. Which includes derivation, numerical solutions for both methods, differentiation between forward and backward methods, applications used in real life, and advantages and disadvantages, given with its result that which one is more efficient. We have also given the references we have used for this review paper.

Keywords: Newton’s Forward Method, Newton’s Backward Method, Mathematical Solution, Derivation, MATLAB Program, C++ Program, Differentiate between Forward and Backward.

Abstract: The main objective of this paper is to explain the comparison between Euler’s method and the Modified Euler’s Method to solve the Ordinary Differential Equation (ODE) numerically and their applications in different fields of engineering. Euler and Modified Euler techniques have been implemented using different step size and time. Euler's method is used for approximating solutions to certain differential equations and works by approximating a solution curve with line segments.

Keywords: Euler’s method, Modified Euler’s method.

Abstract: In this paper, we have given basic information on ‘Bisection and Newton-raphson method’ which includes derivation and their programs on matlab. newton raphson method can be also be applied to the solution of power flow problem when the bus voltage is expressed in polar form & bisection method is can be used to achieve the exact solution when all the parameters are reconstructed.

Keywords: Convergence, Roots, Algorithm, Iterations, Bisection method, Newton-Raphson method, and function, Matlab code

Abstract: The main purpose of this article is to find solutions to linear simultaneous equations using iterative methods. The iterative methods include the Jacobi and the Gauss-Seidel methods.

A brief description of the Jacobi method and Gauss-Seidel method is done followed by its derivation and programming in MATLAB. A simple code for both Jacobi and Gauss-Seidel methods is given for understanding and knowledge. A question is solved by both methods and the answer for both is verified as well.

Keywords: Jacobi iterations, Gauss Seidel iterations, Linear Simultaneous Equations

Abstract: Gauss Seidel and Trapezoidal Methods: Derivation, Mathematical Solution, Differentiation between Trapezoidal and Gauss Seidel Methods, Application Used in Real Life, Advantages & Disadvantages are all covered in detail in this article. When using the trapezoidal approach, more iterations result from increasing the number of integration. If we use the Gauss-Seidel technique with more iterations, the resultant value increases after the decimal. Digital computers employ the Gauss-Seidel technique for computation, whereas geological formations use the trapezoidal approach.

Keywords: Trapezoidal Method, Gauss Seidel Method, Application.

Abstract: The paper is about Newton Raphson Method and Secant Method, the secant method and the newton Raphson method is very effective numerical procedure used for solving non - linear equations of the form f(x)=0. which is all- inclusive to solve the non-square and non-linear problem. It represents a new approach of calculation using nonlinear equation, this paper also discusses the difference between both the methods also the advantages and disadvantages the derivation Newton Raphson formula, algorithm, use and drawbacks of Newton Raphson Method have also been discussed. Secant method is derived via linear Interpolation we provides its error in closed form and analyze its order of Convergence is greater than that of these cant method, and it increases as k Increases.

Keywords: Convergence, non-linear problems.

Abstract: Total 300 samples was the target population of the study. The household survey was undertaken from the beneficiaries of PMUY. Women empowerment variables selected as Involvement in managing the budget , Active participation in decision-making in society and family , Easy access to market, Improvement in confidence level and , Participation in community programmes and events. The dimension of Pradhan Mantri Ujjwala Yojana (PMUY) Scheme selected as Sustainability, Energy Affordability, Accessibility, Safety, environment-friendly and Health & hygiene. Empowering women is essential to the health and social development of families, communities and countries. When women are living safe, fulfilled and productive life, they can reach their full potential, contributing their skills to the workforce and can raise happier and healthier children. The population of the research consists of the beneficiaries of Pradhan Mantri Ujjwala Yojana (PMUY) Scheme are living in Aurangabad District. The data was collected through demographic information and interview schedule from women residing in the rural sector in Aurangabad district of Maharashtra. Descriptive statistics, Chi-square and Regression analysis (By using SPSS) will be used for data processing. The results of the study indicate that, the Sustainability was correlated with Involvement in managing the budget, Active participation in decision-making in society and family,Easy access to market, Improvement in confidence level and Participation in community programmes and events . The result shows the Pradhan Mantri Ujjwala Yojana (PMUY) was not regressed on the predictor women empowerment with respect to Managerial skills.

Keywords: Managing the budget, Active participation in decision-making , Easy access to market, Improvement in confidence level and Participation in community programmes

Abstract: For solving nonlinear equations of the form f(x) = 0, two highly efficient numerical techniques are used: the regula falsi, Newton-Raphson methods. They are obtained using techniques for linear interpolation. Their studies can be completed by utilising Newton's interpolation formula, divided differences, and interpolation theory. We integrate these studies. The information should also be a helpful exercise or example for the usage of split differences and polynomial interpolation in introductory courses in numerical analysis. In this text we have compared the two methods and their functions.

Abstract: In this paper solution of non-linear system of equations is examined by Newton’s method in one variable and in two variables. Rate of convergence is examined and conclude that Newton’s method converges rapidly When a good approximation is available. At last, we found that a method with a higher rate of convergence may Reach the solution of a system in less iteration in comparison to another method with a slower convergence.

Keywords: Rate of convergence