An index reduction method for linear Hessenberg systems (Q814752)

\textit{E. Babolian} and \textit{M. M. Hosseini} [Appl. Math. Comput. 140, No.~1, 77--90 (2003; Zbl 1042.65067)] proposed an index reduction for a special class of systems of linear differential algebraic equations (DAEs) with index \(m+1\). A pseudospectral method based on Chebyshev polynomials of first kind was introduced to solve the systems numerically in case of \(m=1\). In the paper at hand, the author generalises this technique to Hessenberg systems with index 2. The index reduction from 2 to 1 is analysed for a semi-explicit system with exactly \(n=3\) equations in the differential part. The author provides the pseudospectral method using Chebyshev polynomials for the specific systems of index 1 as well as index 2. A numerical simulation with an artificial example demonstrates that the accuracy of the method is higher for the equivalent index-1 formulation than for the original index-2 problem, while the number of involved polynomials is fixed. The difference in accuracy between both systems increases the more basis functions are applied in the approximation.