Blow-up collocation solutions of nonlinear homogeneous Volterra integral equations

Abstract

In this paper, collocation methods are used for detecting blow-up solutions of nonlinear homogeneous Volterra–Hammerstein integral equations. To do this, we introduce the concept of “blow-up collocation solution” and analyze numerically some blow-up time estimates using collocation methods in particular examples where previous results about existence and uniqueness can be applied. Finally, we discuss the relationships between necessary conditions for blow-up of collocation solutions and exact solutions.