Carlos Arranz-Simón

activity

20242026

collaborators

5 papers

math.NA2026

Splitting methods for nonlinear SchrÃ¶dinger equation without order reduction

Carlos Arranz-SimÃ³n, BegoÃ±a Cano

A technique is provided in this paper to integrate nonlinear SchrÃ¶dinger equation with time-dependent Dirichlet boundary conditions with high-order Yoshida splittings which are ba…

math.NA2025

Exponential integrators for parabolic problems with non-homogeneous boundary conditions

Carlos Arranz-SimÃ³n, Alexander Ostermann

Exponential Runge-Kutta methods are a well-established tool for the numerical integration of parabolic evolution equations. However, these schemes are typically developed under the…

math.NA2025

Rational methods for abstract linear initial boundary value problems without order reduction

Carlos Arranz-SimÃ³n, BegoÃ±a Cano, CÃ©sar Palencia

Given an $A$ -stable rational approximation to $e^{z}$ of order $p$ , numerical procedures are suggested to time integrate abstract, well-posed IBVPs, with time-dependent source term $…

math.NA2025

Rational methods for abstract semilinear problems without order reduction

Rational methods are intended to time integrate linear homogeneous problems. However, their scope can be extended so as to cover linear nonhomogeneous problems. In this paper the i…

math.NA2024

Rational methods for abstract linear, non-homogeneous problems without order reduction

Carlos Arranz-SimÃ³n, Cesar Palencia

Starting from an A-stable rational approximation to $e^{z}$ of order $p$ , $r (z) = 1 + z + \dots + z^{p} / p! + O (z^{p + 1}),$ families of stable methods are proposed to time discreti…