Algebraic theory of transformation of linear differential equations

Linear Differential Algebraic Equations with Constant Coefficients

Differential-algebraic equations (DAEs) arise in a variety of applications. Their analysis and numerical treatment, therefore, plays an important role in modern mathematics. The paper gives an introduction to the topics of DAEs. Examples of DAEs are considered showing their importance for practical problems. Some essential concepts that are really essential for understanding the DAE systems are...

Transformation of Differential Algebraic Array Equations to Index One Form

Several new algorithms are proposed that in effect transform DAEs (Differential Algebraic Equations) to a special index one form that can be simulated with standard DAE integrators. The transformation to this form is performed without solving linear and/or nonlinear equation systems, the sparsity of the equations is kept, and array equations remain array equations or differentiated versions of ...

Galois Theory of Linear Differential Equations

Galois Theory of Linear Differential Equations - ReadingSample

Ela Characterization of Classes of Singular Linear Differential-algebraic Equations∗

Linear, possibly overor underdetermined, differential-algebraic equations are studied that have the same solution behavior as linear differential-algebraic equations with well-defined strangeness index. In particular, three different characterizations are given for differential-algebraic equations, namely by means of solution spaces, canonical forms, and derivative arrays. Two levels of general...