When a system is found to have an index greater than 1, NDSolve generates a message and number of steps need to be taken in order to solve the DAE.Īs a first step for high-index DAEs, the index of the system needs to be reduced. NDSolve can be instructed to perform that index reduction. The DAE solver methods built into NDSolve work with index-1 systems, so for higher-index systems an index reduction may be necessary to get a solution. The index of a DAE is the number of times needed to differentiate the DAEs to get a system of ODEs. Generally, a system of DAEs can be converted to a system of ODEs by differentiating it with respect to the independent variable. The flow chart shown below indicates the general process associated with solving DAEs in NDSolve.įlow chart of steps involved in solving DAE systems in NDSolve. Solving systems of DAEs often involves many steps. Such variables are often referred to as algebraic variables. For example, the following equationĭoes not explicitly contain any derivatives of. In fact, derivatives of some of the dependent variables typically do not appear in the equations. With differential-algebraic equations (DAEs), the derivatives are not, in general, expressed explicitly. As long as the function has sufficient continuity, a unique solution can always be found for an initial value problem where the values of the dependent variables are given at a specific value of the independent variable. The derivatives of the dependent variables are expressed explicitly in terms of the independent transient variable and the dependent variables. In general, a system of ordinary differential equations (ODEs) can be expressed in the normal form,
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