Periodic solutions of certain large-scale systems of ODEs can be computed ee-ciently using a hybrid Newton{Picard scheme, especially in a continuation context. In this paper we describe and analyse how this approach can be extended to the direct computation of period doubling bifurcation points. The Newton{Picard scheme is based on shooting and a splitting of the state space in a low-dimensiona...

Recently Bai and Yang in [On HSS-based iteration methods for weakly nonlinear systems, Appl. Numer. Math. 59 (2009) 2923–2936.] proposed the Picard-HSS iteration method to solve the system of nonlinear equations Ax = φ(x), where A ∈ Cn×n is a nonHermitian positive definite matrix and φ : D ⊂ C → C is continuously differentiable function defined on the open complex domain D in the n-dimensional ...

In this paper we define the notions of Ulam-Hyers stability on KST spaces and cwweakly Picard operator for the multivalued operators case in order to establish a relation between these.

In this note, we aim to present some properties of the space of all weakly fuzzy bounded linear operators, with the Bag and Samanta’s operator norm on Felbin’s-type fuzzy normed spaces. In particular, the completeness of this space is studied. By some counterexamples, it is shown that the inverse mapping theorem and the Banach-Steinhaus’s theorem, are not valid for this fuzzy setting. Also...

In this paper we are concerned with a general class of positive linear operators of discrete type. Based on the results of the weakly Picard operators theory our aim is to study the convergence of the iterates of the defined operators and some approximation properties of our class as well. Some special cases in connection with binomial type operators are also revealed.

In this paper, we present a numerical method for solving nonlinear Hammerstein fractional integral equations. The approximates the solution by Picard iteration together with integration designed weakly singular integrals. Error analysis of proposed is also investigated. Numerical examples approve its efficiency in terms accuracy and computational cost.