On some fixed point theorems for multi-valued operators by altering distance techique
AbstractThe aim of this paper is to present some sufficient conditions for the existence and uniqueness of fixed points for…
Fixed point theorems for generalized contraction mappings on b-rectangular metric spaces
AbstractIn the present article, we study some fixed point theorems for a hybrid class of generalized contractive operators in the…
On new faster fixed point iterative schemes for contraction operators and comparison of their rate of convergence in convex metric spaces
AbstractIn this paper we present new iterative algorithms in convex metric spaces. We show that these iterative schemes are convergent…
Avenues for the use of cellular automata in image segmentation
AbstractThe majority of Cellular Automata (CA) described in the literature are binary or three-state. While several abstractions are possible to…
Interval-state cellular automata and their applications to image segmentation
AbstractWe present a new type of optimization algorithms, adapted for neural network training. These algorithms are based upon sequential operator…
Accurate Chebyshev collocation solutions for the biharmonic eigenproblem on a rectangle
AbstractWe are concerned with accurate Chebyshev collocation (ChC) solutions to fourth order eigenvalue problems. We consider the 1D case as…
Invariant sets and attractors for Hanusse-type chemical systems with diffusions
AbstractWe are concerned with Hanusse-type chemical models with diffusions. We show that some bounded invariant sets ⊂R^{N} found for the…
An application of the Picard operator technique to functional integral equations
Abstract In this paper we consider a functional integral equation of the form \[ x(t)=g(t,x(t),x(h(t)))+\int_{a}^{t} f(s,x(h(s)))ds+\int_{a}^{b} K(s,x(h(s)))ds, \ \ t…
Analysis of a rate-and-state friction problem with viscoelastic materials
AbstractWe consider a mathematical model which describes the frictional contact between a viscoelastic body and a foundation. The contact is…
All roots spectral methods: Constraints, floating point arithmetic and root exclusion
Abstract The nonlinear two-point boundary value problem (TPBVP for short) \[u_{xx}+u^{3}=0,\quad u(0)=u(1)=0,\] offers several insights into spectral methods. First, it…
Publications
Diffusion in Random Fields. Applications to Transport in Groundwater
Book summaryA self-consistent theory of stochastic modeling of groundwater systems is presented. Mathematical theory is illustrated and complemented by numerical methods and simulation codes. doi: http://doi.org/10.1007/978-3-030-15081-5 book on publisher website…
Read More Methods of Newton and Newton-Krylov type
Books, Chebyshev method, Convergence orders, divided differences, eigenvalue/eigenvector problems, history, inexact/perturbed iterations, iterative methods, Krylov methods, linear systems in Rn, local convergence, Newton method, nonlinear systems in Rn, Numerical Analysis, secant/chord method, successive approximations
Book summaryLocal convergence results on Newton-type methods for nonlinear systems of equations are studied. Solving of large linear systems by Krylov methods (GMRES, GMBACK, MINPERT) are also dealt with, as…
Read More Solutions with a prescribed interval of positivity for differential systems with nonlocal conditions
AbstractBased on fixed point index, the paper develops a theory of existence, localization and multiplicity of solutions to first-order differential systems subject to linear nonlocal conditions. The main features concern…
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