##
**An enhanced fictitious time integration method for non-linear algebraic equations with multiple solutions: boundary layer, boundary value and eigenvalue problems.**
*(English)*
Zbl 1231.65136

Summary: When problems in engineering and science are discretized, algebraic equations appear naturally. In a recent paper by Liu and Atluri, non-linear algebraic equations (NAEs) were transformed into a nonlinear system of ODEs, which were then integrated by a method labelled as the Fictitious Time Integration Method (FTIM). In this paper, the FTIM is enhanced, by using the concept of a repellor in the theory ofnonlinear dynamical systems, to situations where multiple-solutions exist. We label this enhanced method as MSFTIM. MSFTIM is applied and illustrated in this paper through solving boundary-layer problems, boundary-value problems, and eigenvalue problems with multiple solutions.

### MSC:

65L99 | Numerical methods for ordinary differential equations |