Linearly Implicit Discrete Event Methods for Stiff ODEs. Part I: Theory
نویسندگان
چکیده
This paper introduces two new numerical methods for integration of stiff ordinary differential equations. Following the idea of quantization based integration, i.e., replacing the time discretization by state quantization, the new methods perform first and second order backward approximations allowing to simulate stiff systems. It is shown that the new algorithms satisfy the same theoretical properties of the previous methods. A companion paper with applications illustrate the practical advantages of the methodology. Keywords— Stiff System Simulation, Quantization Based Integration, DEVS
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Linearly Implicit Discrete Event Methods for Stiff ODEs. Part II: Implementation
This second part deals with the main practical issues of the linearly implicit quantization based integration (QBI) methods defined in the companion paper. The translation of the new algorithms into a discrete event (DEVS) specification and its implementation in a DEVS simulation tool is discussed. The efficience of the methods is illustrated comparing the simulation of two examples with the cl...
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