Stable numerical-analytical method for superstiff differential-algebraic equations

The numerical-analytical representation forms of differential-algebraic equations (DAE) solutions through peer representations of spectral components, i.e. skeletal product of matrix pencils eigenvectors, are considered. Method of complete DAE solution calculation for equations with index greater than 1 are presented. The DAE superstiffness phenomenon and its properties are described. It is shown that catastrophic computational noise appears when an inverse Laplace transformation is applied to the complex signal that has no simple Laplace transform. Special time transformation is proposed, that allows to convert Taylor series into series of exponents with divisible real index. Theoretical basis is presented, programs for analytical and numerical production of these exponential series and experimental results are described.