Population projections for AIDS using an actuarial model

1989 ◽  
Vol 325 (1226) ◽  
pp. 99-112 ◽  
Keyword(s):  
Differential Equations ◽  
Numerical Solution ◽  
Numerical Results ◽  
Population Projections ◽  
England And Wales ◽  
Actuarial Model ◽  
Homosexual Transmission

This paper gives details of a model for forecasting aids, developed for actuarial purposes, but used also for population projections. The model is only appropriate for homosexual transmission, but it is age-specific, and it allows variation in the transition intensities by age, duration in certain states and calendar year. The differential equations controlling transitions between states are defined, the method of numerical solution is outlined, and the parameters used in five different Bases of projection are given in detail. Numerical results for the population of England and Wales are shown.

Using the generalized Adams-Bashforth-Moulton method for obtaining the numerical solution of some variable-order fractional dynamical models

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Mohamed M. Khader
Keyword(s):  
Differential Equations ◽  
Fractional Derivative ◽  
Numerical Solution ◽  
Numerical Results ◽  
Convergence Order ◽  
Variable Order ◽  
Numerical Treatment ◽  
Dynamical Models ◽  
Fractional Modeling ◽  
Dynamics Problems

AbstractThis paper is devoted to introduce a numerical treatment using the generalized Adams-Bashforth-Moulton method for some of the variable-order fractional modeling dynamics problems, such as Riccati and Logistic differential equations. The fractional derivative is described in Caputo variable-order fractional sense. The obtained numerical results of the proposed models show the simplicity and efficiency of the proposed method. Moreover, the convergence order of the method is also estimated numerically.

scholarly journals Numerical Solution of Nonlinear Fractional Volterra Integro-Differential Equations via Bernoulli Polynomials

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
Emran Tohidi ◽  
M. M. Ezadkhah ◽  
S. Shateyi
Keyword(s):  
Differential Equations ◽  
Numerical Solution ◽  
Linear Combination ◽  
Fractional Order ◽  
Bernoulli Polynomials ◽  
Approximate Solutions ◽  
Computational Approach ◽  
Numerical Results ◽  
Algebraic Equations

This paper presents a computational approach for solving a class of nonlinear Volterra integro-differential equations of fractional order which is based on the Bernoulli polynomials approximation. Our method consists of reducing the main problems to the solution of algebraic equations systems by expanding the required approximate solutions as the linear combination of the Bernoulli polynomials. Several examples are given and the numerical results are shown to demonstrate the efficiency of the proposed method.

scholarly journals A New Two Derivative FSAL Runge-Kutta Method of Order Five in Four Stages

2020 ◽  
Vol 17 (1) ◽  
pp. 0166
Author(s):  
Hussain Et al.
Keyword(s):  
Differential Equations ◽  
Numerical Solution ◽  
Ordinary Differential Equations ◽  
Numerical Results ◽  
New Method ◽  
Kutta Method ◽  
First Order ◽  
Runge Kutta Method ◽  
Runge Kutta ◽  
The Stability

A new efficient Two Derivative Runge-Kutta method (TDRK) of order five is developed for the numerical solution of the special first order ordinary differential equations (ODEs). The new method is derived using the property of First Same As Last (FSAL). We analyzed the stability of our method. The numerical results are presented to illustrate the efficiency of the new method in comparison with some well-known RK methods.

Stress and Displacement Analysis of a Shell Intersection

1970 ◽  
Vol 92 (2) ◽  
pp. 303-308 ◽  
Author(s):  
K. C. Pan ◽  
R. E. Beckett
Keyword(s):  
Differential Equations ◽  
Boundary Conditions ◽  
Internal Pressure ◽  
Numerical Solution ◽  
Numerical Computation ◽  
Cylindrical Shells ◽  
Numerical Results ◽  
Radius Ratio ◽  
Displacement Analysis

The problem of two normally intersecting cylindrical shells subjected to internal pressure is considered. The differential equations used for the shells are solved subject to the boundary conditions imposed along the intersection between the two cylinders. Details of a procedure for obtaining a numerical solution are given. Numerical results for a radius ratio of 1:2 are presented. Problems encountered in the numerical computation are discussed and the results of the analysis are compared with experiment.

scholarly journals Novel Exponentially Fitted Two-Derivative Runge-Kutta Methods with Equation-Dependent Coefficients for First-Order Differential Equations

2016 ◽  
Vol 2016 ◽  
pp. 1-6
Author(s):  
Yanping Yang ◽  
Yonglei Fang ◽  
Xiong You ◽  
Bin Wang
Keyword(s):  
Differential Equations ◽  
Numerical Solution ◽  
Numerical Results ◽  
First Order ◽  
Truncation Errors ◽  
New Methods ◽  
Exponentially Fitted ◽  
Runge Kutta ◽  
First Order Differential Equations

The construction of exponentially fitted two-derivative Runge-Kutta (EFTDRK) methods for the numerical solution of first-order differential equations is investigated. The revised EFTDRK methods proposed, with equation-dependent coefficients, take into consideration the errors produced in the internal stages to the update. The local truncation errors and stability of the new methods are analyzed. The numerical results are reported to show the accuracy of the new methods.

Numerical Solution of Volterra Integro-Differential Equations Using Improved Runge-Kutta Methods

2019 ◽  
Vol 892 ◽  
pp. 193-199
Author(s):  
Faranak Rabiei ◽  
Fatin Abd Hamid ◽  
Nafsiah Md Lazim ◽  
Fudziah Ismail ◽  
Zanariah Abdul Majid
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Numerical Solution ◽  
Quadrature Rule ◽  
Numerical Results ◽  
Test Problems ◽  
Kutta Method ◽  
Runge Kutta Method ◽  
Runge Kutta ◽  
Interpolation Polynomials

In this paper, we proposed the numerical solution of Volterra integro-differential equations of the second kind using Improved Runge-Kutta method of order three and four with 2 stages and 4 stages, respectively. The improved Runge-kutta method is considered as two-step numerical method for solving the ordinary differential equation part and the integral operator in Volterra integro-differential equation is approximated using quadrature rule and Lagrange interpolation polynomials. To illustrate the efficiency of proposed methods, the test problems are carried out and the numerical results are compared with existing third and fourth order classical Runge-Kutta method with 3 and 4 stages, respectively. The numerical results showed that the Improved Runge-Kutta method by achieving the higher accuracy performed better results than existing methods.

Prison population projections, 2006-2013: England and Wales

2006 ◽  
Author(s):  
Nisha de Silva ◽  
Paul Cowell ◽  
Terence Chow ◽  
Paul Worthington
Keyword(s):  
Prison Population ◽  
Population Projections ◽  
England And Wales
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