scholarly journals On a Retarded Nonlocal Ordinary Differential System with Discrete Diffusion Modeling Life Tables

Mathematics ◽  
2021 ◽  
Vol 9 (3) ◽  
pp. 220
Author(s):  
Francisco Morillas ◽  
José Valero
Keyword(s):  
Numerical Simulation ◽  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Differential System ◽  
Infinite Number ◽  
Life Tables ◽  
Diffusion Modeling ◽  
Ordinary Differential System ◽  
Finite Delay ◽  
Non Local

In this paper, we consider a system of ordinary differential equations with non-local discrete diffusion and finite delay and with either a finite or an infinite number of equations. We prove several properties of solutions such as comparison, stability and symmetry. We create a numerical simulation showing that this model can be appropriate to model dynamical life tables in actuarial or demographic sciences. In this way, some indicators of goodness and smoothness are improved when comparing with classical techniques.

A non-standard numerical approach to the solution of some second-order ordinary differential equations

2015 ◽  
Vol 08 (04) ◽  
pp. 1550076 ◽  
Author(s):  
A. Adesoji Obayomi ◽  
Michael Olufemi Oke
Keyword(s):  
Differential Equation ◽  
Ordinary Differential Equation ◽  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Numerical Approach ◽  
Local Approximation ◽  
Second Order ◽  
Discrete Models ◽  
Order Ordinary Differential Equation ◽  
Non Local

In this paper, a set of non-standard discrete models were constructed for the solution of non-homogenous second-order ordinary differential equation. We applied the method of non-local approximation and renormalization of the discretization functions to some problems and the result shows that the schemes behave qualitatively like the original equation.

ON A METHOD FOR SOLVING A FAMILY OF NONLINEAR BOUNDARY VALUE PROBLEMS FOR ORDINARY DIFFERENTIAL EQUATIONS

2021 ◽  
Vol 73 (1) ◽  
pp. 70-75
Author(s):  
S.M. Temesheva ◽  
◽  
P.B. Abdimanapova ◽  
Keyword(s):  
Differential Equations ◽  
Boundary Value Problem ◽  
Ordinary Differential Equations ◽  
Boundary Value Problems ◽  
Hyperbolic Equations ◽  
Boundary Value ◽  
Point Boundary ◽  
Local Boundary ◽  
The Family ◽  
Non Local

In this paper, we consider a boundary value problem for a family of linear differential equations that obey a family of nonlinear two-point boundary conditions. For each fixed value of the family parameter, the boundary value problem under study is a nonlinear two-point boundary value problem for a system of ordinary differential equations. Non-local boundary value problems for systems of partial differential equations, in particular, non-local boundary value problems for systems of hyperbolic equations with mixed derivatives, can be reduced to the family of boundary value problems for ordinary differential equations. Therefore, the establishment of solvability conditions and the development of methods for solving a family of boundary value problems for differential equations are actual problems. In this paper, using the ideas of the parametrization method of D. S. Dzhumabaev, which was originally developed to establish the signs of unambiguous solvability of a linear two-point boundary value problem for a system of ordinary equations, a method for finding a numerical solution to the problem under consideration is proposed.

scholarly journals Study of Lotka–Volterra Biological or Chemical Oscillator Problem Using the Normalization Technique: Prediction of Time and Concentrations

Mathematics ◽  
2020 ◽  
Vol 8 (8) ◽  
pp. 1324
Author(s):  
Juan Francisco Sánchez-Pérez ◽  
Manuel Conesa ◽  
Iván Alhama ◽  
Manuel Cánovas
Keyword(s):  
Numerical Simulation ◽  
Phase Diagram ◽  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Normalization Procedure ◽  
Limit Values ◽  
Physical Understanding ◽  
Dimensionless Groups ◽  
Dimensionless Variables ◽  
Chemical Oscillator

The normalization of dimensionless groups that rule the system of nonlinear coupled ordinary differential equations defined by the Lotka–Volterra biological or chemical oscillator has been derived in this work by applying a normalized nondimensionalization protocol. The normalization procedure, which is quite accurate, does not require complex mathematical steps; however, a deep physical understanding of the problem is required to choose the appropriate references to define the dimensionless variables. From the dimensionless groups derived, the functional dependences of some unknowns of interest are established. Due to the coupled nature of the problem that induces temporal concentration rates of each species that are quite different at each point of the phase diagram, this diagram has been divided into four stretches corresponding to the four quadrants. For each stretch, the limit values (maximum or minimum) of the variables, as well as their duration, are expressed in terms of the dimensionless groups derived before. Finally, to check all the mentioned dependences, a numerical simulation has been carried out.

scholarly journals Numerical Simulation and Symmetry Reduction of a Two-Component Reaction-Diffusion System

2020 ◽  
Vol 2020 ◽  
pp. 1-5
Author(s):  
Jina Li ◽  
Xuehui Ji
Keyword(s):  
Numerical Simulation ◽  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Reaction Diffusion ◽  
Symmetry Reduction ◽  
Reaction Diffusion System ◽  
Diffusion System ◽  
Symmetry Classification ◽  
Two Component

In this paper, the symmetry classification and symmetry reduction of a two-component reaction-diffusion system are investigated, the reaction-diffusion system can be reduced to system of ordinary differential equations, and the solutions and numerical simulation will be showed by examples.

Analogical Modeling and Numerical Simulation for Sintering Phenomena

2013 ◽  
Vol 436 ◽  
pp. 127-136 ◽  
Author(s):  
Corina Bokor ◽  
Vlad Mureşan ◽  
Toderiţa Nemeş ◽  
Claudiu Isarie
Keyword(s):  
Numerical Simulation ◽  
Partial Differential Equations ◽  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Analytical Solutions ◽  
Experimental Methods ◽  
Science And Engineering ◽  
Physical Phenomena ◽  
Material Powder

In this paper the authors propose an approach for analogical modeling and numerical simulation of the phenomena of sintering, taking into account different cases depending on the type of energy used in the process of aggregation and the nature of the material powder, using a software which simulates the propagation and the control of the temperature. Many physical phenomena encountered in science and engineering can be described mathematically through partial differential equations (PDE) and ordinary differential equations (ODE) such as propagation phenomena, engineering applications, hydrotechnics, chemistry, pollution a.s.o. There may be situations when the exact establish of the analytical solutions becomes difficult or impossible for arbitrary shapes. In these cases the determination of some approximant solution through experimental methods, that have to verify with acceptable errors, the PDE expression specified to the studied phenomenon, is justified.

scholarly journals A high order numerical method for solving Caputo nonlinear fractional ordinary differential equations

2021 ◽  
Vol 6 (12) ◽  
pp. 13187-13209
Author(s):  
Xumei Zhang ◽  
◽  
Junying Cao
Keyword(s):  
Numerical Simulation ◽  
Theoretical Analysis ◽  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Lagrange Interpolation ◽  
Numerical Scheme ◽  
Truncation Error ◽  
Interpolation Method ◽  
High Order ◽  
Local Truncation Error

<abstract><p>In this paper, we construct a high order numerical scheme for Caputo nonlinear fractional ordinary differential equations. Firstly, we use the piecewise Quadratic Lagrange interpolation method to construct a high order numerical scheme for Caputo nonlinear fractional ordinary differential equations, and then analyze the local truncation error of the high order numerical scheme. Secondly, based on the local truncation error, the convergence order of $ 3-\theta $ order is obtained. And the convergence are strictly analyzed. Finally, the numerical simulation of the high order numerical scheme is carried out. Through the calculation of typical problems, the effectiveness of the numerical algorithm and the correctness of theoretical analysis are verified.</p></abstract>

scholarly journals Optimal Control for Transmission of Water Pollutants

2018 ◽  
Vol 3 (4) ◽  
pp. 381-391 ◽  
Author(s):  
Nita H. Shah ◽  
Shreya N. Patel ◽  
Moksha H. Satia ◽  
Foram A. Thakkar
Keyword(s):  
Numerical Simulation ◽  
Mathematical Model ◽  
Optimal Control ◽  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Waste Materials ◽  
Chemical Plants ◽  
Water Pollutants ◽  
Linear Ordinary Differential Equations ◽  
Oil Gas

Pollutants are formed when oil, gas, chemical plants, etc. discharge their harmful waste materials into stream or other water bodies. In this paper, a mathematical model for water pollutants which are soluble and insoluble has been formulated as a system of non-linear ordinary differential equations. Control is applied on insoluble water pollutants to process them into soluble water pollutants. Numerical simulation has been carried out which suggest that soluble water pollutants are increasing as compared to insoluble water pollutants.

Sign in / Sign up

Export Citation Format

Share Document