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oapen-20.500.12657-472052021-03-11T09:44:25Z Introduction to Mathematical Modeling and Computer Simulations Mityushev, Vladimir Nawalaniec, Wojciech Rylko, Natalia mathematics number systems 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. 2021-03-11T09:30:29Z 2021-03-11T09:30:29Z 2018 book https://library.oapen.org/handle/20.500.12657/47205 eng Taylor & Francis Routledge 7b3c7b10-5b1e-40b3-860e-c6dd5197f0bb dcdfa5c8-54de-4269-8ce0-03e32337f3d4 041900c8-f00e-4c78-9cb6-7d5015e5508a Routledge 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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