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oapen-20.500.12657-472072021-03-12T01:58:14Z Chapter 1 Principles of Mathematical Modeling Mityushev, Vladimir Nawalaniec, Wojciech Rylko, Natalia Advanced, Analysis, Applications, Asymptomatic, Principals, Vector, Calculus, Classics, Composites, Computations, Dimensional, Equations, General, Heat, Introduction, Mathematics Mechanical, Methods, Numercal, ODEs, Simulations, Stochastic, Symbolic, Stationary bic Book Industry Communication::P Mathematics & science::PB Mathematics bic Book Industry Communication::P Mathematics & science::PB Mathematics::PBC Mathematical foundations::PBCN Number systems Mathematical Modeling describes a process and an object by use of the mathematical language. A process or an object is presented in a "pure form" in Mathematical Modeling when external perturbations disturbing the study are absent. Computer simulation is a natural continuation of the Mathematical Modeling. Computer simulation can be considered as a computer experiment which corresponds to an experiment in the real world. Such a treatment is rather related to numerical simulations. Symbolic simulations yield more than just an experiment. Mathematical Modeling of stochastic processes is based on the probability theory, in particular, that leads to using of random walks, Monte Carlo methods and the standard statistics tools. Symbolic simulations are usually realized in the form of solution to equations in one unknown, to a system of linear algebraic equations, both ordinary and partial differential equations (ODE and PDE). Various mathematical approaches to stability are discussed in courses of ODE and PDE. 2021-03-11T09:44:18Z 2021-03-11T09:44:18Z 2018 chapter https://library.oapen.org/handle/20.500.12657/47207 eng application/pdf Attribution-NonCommercial-NoDerivatives 4.0 International 9781315277240_oachapter1.pdf Taylor & Francis Introduction to Mathematical Modeling and Computer Simulations Routledge 7b3c7b10-5b1e-40b3-860e-c6dd5197f0bb 65bb0d0f-5cf4-4a63-b1ba-394b9b53b24f Routledge 25 open access
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Mathematical Modeling describes a process and an object by use of the mathematical language. A process or an object is presented in a "pure form" in Mathematical Modeling when external perturbations disturbing the study are absent. Computer simulation is a natural continuation of the Mathematical Modeling. Computer simulation can be considered as a computer experiment which corresponds to an experiment in the real world. Such a treatment is rather related to numerical simulations. Symbolic simulations yield more than just an experiment. Mathematical Modeling of stochastic processes is based on the probability theory, in particular, that leads to using of random walks, Monte Carlo methods and the standard statistics tools. Symbolic simulations are usually realized in the form of solution to equations in one unknown, to a system of linear algebraic equations, both ordinary and partial differential equations (ODE and PDE). Various mathematical approaches to stability are discussed in courses of ODE and PDE.
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