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System Solver: an open source tool for mathematically modelling dynamical systems
System-Solver: una herramienta de código abierto para la modelación de sistemas dinámicos
Keywords:
ODE solver, computational differentiation, modelling, dynamical system (en)ODE Solver, diferenciación por computadoras, modelación, sistema dinámicos (es)
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The following paper presents a freeware modelling tool simulating dynamic systems that can be represented by either an ordinary differential equation (ODE) or a set of differential equations of different orders. The main idea leading to this software development is related to the fact that many physical, biological, ecological, economical, chemical, social and engineering problems can be expressed in this way. Furthermore, the solution to these problems requires some expertise in numerical methods and programming. Such knowledge is uncommon in some of the experts in such scientific domains. A tool to fill in this knowledge gap, increase productivity within modelling-related research and support the teaching of mathematical modelling topics is thus needed. This paper introduces System Solver, a computer application that facilitates the formulation of initial value problems for ODE systems, numerically solves these problems and provides a user with not only the solution but also debugged Visual Basic source code for the application. The obtained code can be easily shared among researchers, which facilitates the replication of numerical experiments even across different operating systems. This software's introduction is accompanied by examples from different domains, including one example from stochastic modelling.
En este artículo se presenta una herramienta de código abierto para la simulación de sistemas dinámicos, representados a través de ecuaciones diferenciales de distinto orden o de sistemas de ecuaciones diferenciales ordinarias (EDO). La idea principal que incentivó el desarrollo de esta herramienta consiste en que muchos procesos físicos, biológicos, ecológicos, económicos, químicos y sociales, y un sinnúmero de problemas ingenieriles, pueden ser expresados de esta forma. Adicionalmente, la solución de ese tipo de problemas exige experticia en métodos numéricos y programación. Este tipo de experticia no es muy común para los expertos de las áreas mencionadas; por ello, se requiere de una herramienta que permita sortear esta falta de experticia e incrementar la productividad en trabajos relacionados con tópicos de modelación. System-Solver es una aplicación que facilita la formulación de problemas de valor inicial en EDO y su solución numérica, y mediante un programa en Visual Basic la automatiza. El programa obtenido se puede compartir fácilmente con otros investigadores, facilitando la reproducción del ejercicio de modelación incluso en diferentes sistemas operativos. La presentación del software está acompañada con ejercicios de diversas áreas temáticas, incluyendo un ejemplo de modelación estocástica.
References
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Copyright (c) 2010 Efraín Domínguez, Felipe Ardila, Santiago Bustamante
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