Abstract
In the last few decades, stiff differential equations have attracted a great deal of interest from academic society, because much of the real life is covered by stiff behavior. In addition to importance of producing model equations, capturing an exact behavior of the problem by dealing with a solution method is also handling issue. Although there are many explicit and implicit numerical methods for solving them, those methods cannot be properly applied due to their computational time, computational error or effort spent for construction of a structure. Therefore, simulation techniques can be taken into account in capturing the stiff behavior. In this respect, this study aims at analyzing stiff processes through stochastic approaches. Thus, a Monte Carlo based algorithm has been presented for solving some stiff ordinary differential equations and system of stiff linear ordinary differential equations. The produced results have been qualitatively and quantitatively discussed.
Highlights
Differential equations are used to model real-life systems by conserving their physical structures
While developing a model of a system, it is necessary to consider suddenly occurred reactions with small time steps without neglecting that the system continue to behave over the whole-time interval
Despite natural restrictions of physical systems represented by stiff Ordinary Differential Equations (ODEs), they are commonly used in modelling various problems, through chemical reactions, while creating electrical circuits or studying in control theory etc
Summary
Differential equations are used to model real-life systems by conserving their physical structures. Even though an application area of numerical methods has a broad range, they are occasionally suffering from their restrictions They may be seen to be efficient for the aim of the solving the problems iteratively, but these methods cannot be a first choice considering their computational time, computational error or effort spent for construction of a stiff structure. At this point, new approaches such that simulation techniques emerge by paying attention to these corresponding issues [4,5]. Random sampling and estimation techniques are used in this study to observe the behavior of the stiff differential equations
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More From: An International Journal of Optimization and Control: Theories & Applications (IJOCTA)
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