Ordinary Differential Equations (ODE) are used throughout science where the capture of rates of change in states is sought. While both pieces of commercial and open software exist to study such systems, their efficient and accurate usage frequently requires deep understanding of mathematics and programming. The package we present here, PyGOM, seeks to remove these obstacles for models based on ...

Email: [email protected] Abstract: Traditionally, the concepts of graph theory are applied to design stationary computer networks and, to analyze dynamics of social networks. However, the majority of non-stationary network models are formulated by using Ordinary Differential Equations (ODE) with varying orders having homogeneous or non-homogeneous forms. However, the analysis of continuous ...

MOTIVATION Modeling and analysis of complex systems are important aspects of understanding systemic behavior. In the lack of detailed knowledge about a system, we often choose modeling equations out of convenience and search the (high-dimensional) parameter space randomly to learn about model properties. Qualitative modeling sidesteps the issue of choosing specific modeling equations and frees ...

In the present paper, SIR model tracks numbers of susceptible, infected and recovered individuals during an epidemic with help ordinary differential equations (ODE). First, we give formulation our phenomena. Secondly, a fully discrete difference scheme is derived for model.At end this aper, simulation results model. A comparison obtained numerical both models performed in absence exact solution.

For models described by ordinary differential equation boundary value problems (ODE BVPs), we derive adjoint equations for sensitivity analysis, giving explicit forms for the boundary conditions of the adjoint boundary value problem. The solutions of the adjoint equations are used to efficiently compute gradients of both integral-form and pointwise constraints. Existence and stability results a...

In this paper, we present an approximate method to solve the solution of the second kind Volterra integral equations. This method is based on a previous scheme, applied by Maleknejad ‎et al., ‎‎[K. Maleknejad ‎and Aghazadeh, Numerical solution of Volterra integral equations of the second kind with convolution kernel by using Taylor-series expansion method, ‎Appl. Math. Comput.‎ (2005)]‎ to gain...

This paper presents a new control technique for the EDC thermal cracking furnace modeled by sets of ordinary differential equation (ODE) and 2D-partial differential equations (PDEs). The dynamics of coupled 2DPDEs-ODE model have been divided into 2 subsystems, set of state variables of the internal and external cracking coil. With the concept of input-output (I/O) linearization, these inner and...

although elzaki transform is stronger than sumudu and laplace transforms to solve the ordinary differential equations withnon-constant coefficients, but this method does not lead to finding the answer of some differential equations. in this paper, a method is introduced to find that a differential equation by elzaki transform can be ‎solved?‎

Ordinary differential equations (ODEs) are one of the important topics in engineering mathematics that lead to the understanding of technical concepts among students. This study was conducted to explore the students’ understanding of ODEs when they solve ODE questions using a traditional method as well as a computer algebraic system, particularly Maple. Ten engineering technology students from ...

The SBML ODE Solver Library (SOSlib) is a command-line oriented tool and programming library for construction and numerical integration of a system of ordinary differential equations (ODE) from a chemical reaction network encoded in the Systems Biology Markup Language (SBML). It is written in ANSI C, provides bindings for a variety of scripting languages and is distributed under LGPL license. T...