Two seemingly unrelated problems are intimately connected. The first is the equsingularity problem in R: For an analytic family ft : (R , 0) → (R, 0), when should it be called an “equisingular deformation”? This amounts to finding a suitable trivialization condition (as strong as possible) and, of course, a criterion. The second is on the Morse stability. We define R∗, which is R “enriched” wit...

In the present study, high order compact finite difference methods is used to solve one-dimensional Bratu-type equations numerically. The convergence analysis of the methods is discussed and it is shown that the theoretical order of the method is consistent with its numerical rate of convergence. The maximum absolute errors in the solution at grid points are calculated and it is shown that the ...