The solution of a combustion problem with Rosenbrock methods

ABSTRACT

Solving flame propagation problems with the method of lines leads to large systems of ordinary differential equations. These systems are usually solved by Backward Differentiation Formula (BDF) methods, such as by LSODE of Hindmarsh. Recently, Rosenbrock methods turned out to be rather successful for integrating small systems with inexpensive function and Jacobian evaluations. However, no test has been done on the performance of some recently developed Rosenbrock codes in a situation in which the dimension of the system is large, for example, over one hundred equations. These Rosenbrock codes performed quite well on the STIFF DETEST and other small systems. The aim of this paper is to investigate the performance of the Rosenbrock methods in solving the flame propagation problem by the method of lines.

REFERENCES

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INDEX TERMS

Classification:
  G. Mathematics of Computing
  G.1 NUMERICAL ANALYSIS
      G.1.7 Ordinary Differential Equations
          Subjects: Initial value problems; Stiff equations
      G.1.8 Partial Differential Equations
          Subjects: Method of lines

General Terms:
Performance