Evaluation of overshooting errors in particle methods for diffusion by biased global random walk
AbstractThe adjustment of grid steps which guarantees that particles methods yield no numerical diffusion inevitably induces overshooting errors in the…
On the accuracy of Stoermer/Verlet method as the numerical integrator of the n-body problem – Application to solar system
AbstractThe Newton-Störmer/Verlet-leapfrog method (S/V) is a symplectic and symmetric one of order two, which, when applied to separable Hamiltonian dynamical systems,…
Numerical investigations on ergodicity of solute transport in heterogeneous aquifers
AbstractDarcy velocities for lognormal hydraulic conductivity with small variance and finite correlation length were approximated by periodic random fields. Accurate…
Evaluation of the first‐order approximations for transport in heterogeneous media
AbstractLongitudinal dispersion coefficients in given realizations of the transport computed by two currently used approximations of the first‐order in velocity…
On a compound approximation operator of D.D. Stancu type
AbstractIn this note we consider a linear and positive compound approximation operator of D.D. Stancu type depending of several parameters.…
Rate of approximation for certain Durrmeyer operators
AbstractIn the present note, we study a certain Durrmeyer type integral modification of Bernstein polynomials. We investigate simultaneous approximation and…
Bilateral approximations of solutions of equations by order three Steffensen-type methods
Abstract We study the convergence of a method of Steffensen-type, which is obtained from the Lagrange polynomial of inverse interpolation with…
Bilateral approximations of the roots of scalar equations by Lagrange-Aitken-Steffensen method of order three
Abstract We study the monotone convergence of two general methods of Aitken-Steffenssen type. These methods are obtained from the Lagrange…
On a Steffensen-Hermite type method for approximating the solutions of nonlinear equations
Abstract It is well known that the Steffensen and Aitken-Steffensen type methods are obtained from the chord method, using controlled…
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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