‎In this paper‎, ‎an approach based on statistical spline model (SSM) and collocation method is proposed to solve Volterra-Fredholm integral equations‎. ‎The set of collocation nodes is chosen so that the points yield minimal error in the nodal polynomials‎. ‎Under some standard assumptions‎, ‎we establish the convergence property of this approach‎. ‎Numerical results on some problems are given...

Most, if not all, animals are highly responsive organisms that are capable of adjusting their behaviour during the course of their interactions with others [1]. This observation may seem obvious, yet evolutionary theory has traditionally modelled cooperation and conflict as a ‘sealed bid’, assuming that both parties decide on a fixed strategy without any knowledge of the other’s behaviour [2]. ...

We study the nonsymmetric algebraic Riccati equation whose four coefficient matrices are the blocks of a nonsingular M -matrix or an irreducible singular M -matrix M . The solution of practical interest is the minimal nonnegative solution. We show that Newton’s method with zero initial guess can be used to find this solution without any further assumptions. We also present a qualitative perturb...

? Abstract. In previous papers, the authors studied normalization relative to desirable sets S of`partial results', where it is shown that such sets must be stable. For example, the sets of normal forms, head-normal-forms, and weak head-normal-forms in the-calculus, are all stable. They showed that, for any stable S, S-needed reductions are S-normalizing. This paper continues the investigation ...