Efficient solution of ordinary differential equations with a parametric lexicographic linear program embedded

摘要: This work analyzes the initial value problem in ordinary differential equations with a parametric lexicographic linear program (LP) embedded. The LP is said to be embedded since dynamics depend on solution of LP, which turn parameterized by dynamic states. formulation finds application flux balance analysis, serves as modeling framework for industrial fermentation reactions. It shown that can intractable numerically, arises from fact induces an effective domain may not open. A numerical method developed reformulates system so it defined open set. result semi-explicit index-one algebraic equations, solved efficient and accurate methods. this addresses many issues stemming original problem's intractability. examples processes demonstrates its effectiveness efficiency.