scholarly journals Taylor collocation method for a system of nonlinear Volterra delay integro-differential equations with application to COVID-19 epidemic

2020 ◽  
Author(s):  
Hafida Laib ◽  
Azzeddine Bellour ◽  
Aissa Boulmerka
Keyword(s):  
Differential Equations ◽  
Numerical Solution ◽  
Numerical Method ◽  
Collocation Method ◽  
Mathematical Ecology ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Taylor Polynomials ◽  
Convergent Algorithm ◽  
A Current

Abstract The present paper deals with the numerical solution for a general form of a system of nonlinear Volterra delay integro-differential equations (VDIDEs). The main purpose of this work is to provide a current numerical method based on the use of continuous collocation Taylor polynomials for the numerical solution of nonlinear VDIDEs systems. It is shown that this method is convergent. Numerical results will be presented to prove the validity and effectiveness of this convergent algorithm. We apply two models to the COVID-19 epidemic in China and one for the Predator-Prey model in mathematical ecology.

Numerical Solution to Volterra-Type Integro-Differential Equations of the Second Kinds by Legendre Collocation Method

2014 ◽  
Vol 687-691 ◽  
pp. 1522-1527
Author(s):  
Ting Jing Zhao
Keyword(s):  
Differential Equation ◽  
Exact Solution ◽  
Differential Equations ◽  
Numerical Solution ◽  
Numerical Method ◽  
Collocation Method ◽  
High Accuracy ◽  
Time Step ◽  
Volterra Type ◽  
Legendre Collocation Method

The purpose of this paper is to propose an efficient numerical method for solving Volterra-type integro-differential equation of the second kinds. This method based on Legendre-Gauss-Radau collocation, which is easy to be implemented especially for nonlinear and possesses high accuracy. Also, the method can be done by proceeding in time step by step. Illustrative examples have been discussed to demonstrate the validity and applicability of the technique, and the results have been compared with the exact solution.

scholarly journals Dynamic behaviors of a nonautonomous predator–prey system with Holling type II schemes and a prey refuge

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Yumin Wu ◽  
Fengde Chen ◽  
Caifeng Du
Keyword(s):  
Lyapunov Function ◽  
Differential Equations ◽  
Comparison Theorem ◽  
Sufficient Conditions ◽  
Oscillation Theory ◽  
Type Ii ◽  
Prey Refuge ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Prey System

AbstractIn this paper, we consider a nonautonomous predator–prey model with Holling type II schemes and a prey refuge. By applying the comparison theorem of differential equations and constructing a suitable Lyapunov function, sufficient conditions that guarantee the permanence and global stability of the system are obtained. By applying the oscillation theory and the comparison theorem of differential equations, a set of sufficient conditions that guarantee the extinction of the predator of the system is obtained.

scholarly journals Solving Some Differential Equations Arising in Electric Engineering Using Hermite Polynomials

2020 ◽  
Vol 12 (4) ◽  
pp. 517-523
Author(s):  
G. Singh ◽  
I. Singh
Keyword(s):  
Differential Equations ◽  
Numerical Solution ◽  
Collocation Method ◽  
Hermite Polynomials ◽  
Electric Circuit ◽  
Algebraic Equations ◽  
Numerical Examples ◽  
Electric Engineering ◽  
Collocation Points ◽  
Linear Algebraic Equations

In this paper, a collocation method based on Hermite polynomials is presented for the numerical solution of the electric circuit equations arising in many branches of sciences and engineering. By using collocation points and Hermite polynomials, electric circuit equations are transformed into a system of linear algebraic equations with unknown Hermite coefficients. These unknown Hermite coefficients have been computed by solving such algebraic equations. To illustrate the accuracy of the proposed method some numerical examples are presented.

scholarly journals Sinc Collocation Method for Finding Numerical Solution of Integrodifferential Model Arisen in Continuous Mixed Strategy

2014 ◽  
Vol 2014 ◽  
pp. 1-8
Author(s):  
F. Hosseini Shekarabi
Keyword(s):  
Differential Equations ◽  
Numerical Solution ◽  
Collocation Method ◽  
Mixed Strategy ◽  
Evolutionary Game ◽  
Collocation Methods ◽  
Mixed Strategies ◽  
Algebraic Equations ◽  
New Techniques ◽  
Numerical Tool

One of the new techniques is used to solve numerical problems involving integral equations and ordinary differential equations known as Sinc collocation methods. This method has been shown to be an efficient numerical tool for finding solution. The construction mixed strategies evolutionary game can be transformed to an integrodifferential problem. Properties of the sinc procedure are utilized to reduce the computation of this integrodifferential to some algebraic equations. The method is applied to a few test examples to illustrate the accuracy and implementation of the method.

A Parallel Block Predictor-Corrector Method by Python-Based Distributed Computing

2012 ◽  
Vol 263-266 ◽  
pp. 1315-1318
Author(s):  
Kun Ming Yu ◽  
Ming Gong Lee
Keyword(s):  
Differential Equations ◽  
Numerical Solution ◽  
Numerical Method ◽  
Initial Value Problem ◽  
Message Passing ◽  
Message Passing Interface ◽  
Parallel Structure ◽  
Initial Value ◽  
Speed Up ◽  
Predictor Corrector

This paper is to discuss how Python can be used in designing a cluster parallel computation environment in numerical solution of some block predictor-corrector method for ordinary differential equations. In the parallel process, MPI-2(message passing interface) is used as a standard of MPICH2 to communicate between CPUs. The operation of data receiving and sending are operated and controlled by mpi4py which is based on Python. Implementation of a block predictor-corrector numerical method with one and two CPUs respectively is used to test the performance of some initial value problem. Minor speed up is obtained due to small size problems and few CPUs used in the scheme, though the establishment of this scheme by Python is valuable due to very few research has been carried in this kind of parallel structure under Python.

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