Discretization based indices for semilinear partial differential algebraic equations (Q1294502)

The authors consider semilinear partial differential algebraic equations of the form \[ Au_t+ Bu_{xx}+ F(u)= f(t,x), \] where one or both \(A\) and \(B\) are singular. They define differential time and space indices based on the corresponding semidiscretizations and show that two often-used methods converge for index-one systems.