Zdeněk Šmarda

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A Newton-Kantorovich convergence theorem of a new modified Halley's method family is established in a Banach space to solve nonlinear operator equations. We also present the main results to reveal the competence of our method. Finally, two numerical examples arising in the theory of the radiative transfer, neutron transport and in the kinetic theory of(More)
New explicit results on exponential stability, improving recently published results by the authors, are derived for linear delayed systems ˙ x i (t) = − m ∑ j=1 r ij ∑ k=1 a k ij (t)x j (h k ij (t)), → R are measurable delays. The progress was achieved by using a new technique making it possible to replace the constant 1 by the constant 1 + 1/e on the(More)
The purpose of this paper is to employ an alternative approach to reconstruct the standard variational iteration algorithm II proposed by He, including Lagrange multiplier, and to give a simpler formulation of Adomian decomposition and modified Adomian decomposition method in terms of newly proposed variational iteration method-II (VIM). Through careful(More)
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