On a generalization of the Steffensen method
Abstract We extend the Steffensen method for solving the equation \(f\left( x\right)=0\) to the setting of the Banach spaces, \(f:X\rightarrow…
Posts by Ion Păvăloiu
Remarks on the secant method for the solution of nonlinear operator equations
Abstract Let \(X_{1},X_{2}\) be two Banach spaces and \(f:X_{1}\rightarrow X_{2}\) a nonlinear equation. We study the chord method for solving…
On the convergency of a Steffensen-type method
Abstract Let \(X_{1},X_{2}\) be two Banach spaces, \(f:X_{1}\rightarrow X_{2}\) a nonlinear mapping. We study the convergence of the Steffensen method for…
On the chord method
Abstract Let \(X_{1},X_{2}\) be two Banach spaces, \(f:X_{1}\rightarrow X_{2}\) a nonlinear mapping and consider the chord method for solving the…
On a Steffensen type method for solving nonlinear operator equations
Abstract Let \(X\) be a Banach space, \(Y\) a normed space and the nonlinear operator equation \(P\left( x\right) =0\), where…
On approximating the solutions of equations in metric spaces
Abstract Let \(\left( X,\rho \right)\) be a complete metric space, \(f:X\rightarrow X\) a nonlinear mapping. In order to solve the…
Error estimations in the numerical solving of the systems of equations
Abstract Let \(\left( x_{i},\rho_{i}\right) ,\ i=1,2,\) be two complete metric space and \(F_{1}:X_{1}\times X_{2}\rightarrow X_{1},\ F_{2}:X_{1}\times X_{2}\rightarrow X_{2}\) two nonlinear…
An algorithm in the solving of equations by interpolation
Abstract Consider the nonlinear equation in \(R\), \(f\left( x\right) =0\), where \(f:A\rightarrow B \), \((A,B\subseteq \mathbb{R})\) which is assumed bijective. The Lagrange…
Error estimations in the numerical solving of systems of equations in metric spaces
Abstract Let \(X_{1},X_{2}\) be two complete metric spaces, \(X=X_{1}\times X_{2}\) and the nonlinear mappings \(F_{1}:X\rightarrow X_{1},\ F_{2}:X\rightarrow X_{2}\). In order…
On the error estimation in the numerical convergence of certain iterative methods
Abstract We study the nonlinear equations of the form \[x=\lambda D\left( x\right) +y,\] where \(\lambda \in \mathbb{R}\) and \(y\in E\)…
Publications
Spectral collocation solutions to second order singular Sturm-Liouville eigenproblems
AbstractWe comparatively use some classical spectral collocation methods as well as highly performing Chebfun algorithms in order to compute the eigenpairs of second order singular Sturm-Liouville problems with separated self-adjoint…
Read More Accurate spectral collocation computation of high order eigenvalues for singular Schrödinger equations
AbstractWe are concerned with the study of some classical spectral collocation methods as well as with the new software system Chebfun in computing high order eigenpairs of singular and regular…
Read More Accurate spectral collocation solutions to some Bratu’s type Boundary Value Problems
AbstractWe solve by Chebyshev spectral collocation some genuinely nonlinear Liouville-Bratu-Gelfand type, 1D and a 2D boundary value problems. The problems are formulated on the square domain [−1, 1] × [−1,…
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