Qualitative behavior of stiff ODEs through a stochastic approach

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.