Mariam Sultana

Numerical Solution of Sixth-Order Differential Equations Arising in Astrophysics by Neural Network

In the current paper, a neural network method to solve sixth-order differential equations and their boundary conditions has been presented. The idea this method incorporates is to integrate knowledge about the differential equation and its boundary conditions into neural networks and the training sets. Neural networks are being used incessantly to solve all kinds of problems hailing a wide range of disciplines. Several examples are given to illustrate the efficiency and implementation of the Neural Network method.

Solving Polluted Lakes System by using Perturbation-Iteration Method

Water pollution is a major global problem that requires ongoing evaluation and revision of water resource policies at all levels, in order to create a healthy living environment. Differential equations are an effective way to analyze such situations. In this paper a system of linear equations with interconnecting pipes is considered for analyzing the pollution of system of lakes through differential equations. Perturbation-iteration method is used to compute an approximate solution of three input models i.e. periodic, linear step model and exponentially decaying model. The fourth order RungeKutta method (RK4) numerical solution of the lakes system problem is used as a reference to compare with the analytical approximations showing the high accuracy of the results.

An Effective Perturbation Iteration Algorithm for Solving Riccati Differential Equations

In the following study, a novel approach called the Perturbation Iteration Algorithm PIA has been proposed and subsequently adopted for deriving and solving the Riccati differential equation. This new Perturbation Iteration Method is efficient and has no requirement of a small parameter assumption as its earlier classical counterparts do. Some examples have been presented to exhibit how simply and efficiently the proposed method works. After deriving the exact solution of the Riccati equation, the capability and the simplicity of the proposed technique is clarified. A percentage error for each example has also been presented.

A Solution for a Water Quality Model in a Uniform Stream Channel using New Iterative Method

During the last decade, political awareness of river water quality issues has increased significantly. New environmental policies have a requirement for improved methods for the investigation and evaluation of river water quality. Moreover, the derivation and assessment of management practices is also necessary. An efficient Perturbation Iteration Algorithm for solving the water quality assessment model has been developed. The employed equation of this uniform flow model is one-dimensional Advection-DispersionReaction equation that has variable coefficients. This water quality model requires the calculation of the substance dispersion considering the water velocity in the channel. Numerical values are obtained by using the Runge-Kutta-Fehlberg fourth-fifth order method for comparison. It was discovered that Perturbation Iteration Algorithm solution gels well with the numerical solution. Two examples are included to demonstrate the efficiency, accuracy, and simplicity of the proposed method.

Delta : Polynomial Approximation of Time Period 1620–2013

The difference between the Uniform Dynamical Time and Universal Time is referred to as (delta ). Delta is used in numerous astronomical calculations, that is, eclipses,and length of day. It is additionally required to reduce quantified positions of minor planets to a uniform timescale for the purpose of orbital determination. Since Universal Time is established on the basis of the variable rotation of planet Earth, the quantity mirrors the unevenness of that rotation, and so it changes slowly, but rather irregularly, as time passes. We have worked on empirical formulae for estimating and have discovered a set of polynomials of the 4th order with nine intervals which is accurate within the range of ±0.6 seconds for the duration of years 1620–2013.