Numerical comparisons among some methods for Hamiltonian problems
, 2010 We report a few sumerical tests comparing some newly defined energy-preserving integrators and symplectic methods, using either constant and variable stepsize.Comment: 5 pages, 8 ...
Brugnano, Luigi +2 more
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Numerical treatments of nonlinear Burgers–Fisher equation via a combined approximation technique
Kuwait Journal of ScienceA combined spectral matrix collocation strategy is presented to solve the time-dependent nonlinear Burgers–Fisher equation pertaining to various important physical mechanisms such as advection, diffusion, and logistic reaction.
Mohammad Izadi, Hari Mohan Srivastava
doaj +1 more source
Enhanced HBVMs for the numerical solution of Hamiltonian problems with multiple invariants
, 2013 Recently, the class of energy-conserving Runge-Kutta methods named Hamiltonian Boundary Value Methods (HBVMs), has been proposed for the efficient solution of Hamiltonian problems, as well as for other types of conservative problems.
Brugnano, Luigi, Sun, Yajuan
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Analysis and new simulations of fractional Noyes-Field model using Mittag-Leffler kernel
Scientific African, 2022 In this manuscript, the fractional-in-time NoyesField model for Belousov-Zhabotinsky reaction transport is considered with a novel numerical technique, which was used to approximate the Atangana-Baleanu (ABC) operator which models the subdiffusion ...
Berat Karaagac +2 more
doaj
Efficient implementation of Radau collocation methods [PDF]
, 2013 In this paper we define an efficient implementation of Runge-Kutta methods of Radau IIA type, which are commonly used when solving stiff ODE-IVPs problems.
Brugnano, L. +2 more
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An efficient variable stepsize rational method for stiff, singular and singularly perturbed problems
Alexandria Engineering Journal, 2022 In this article, a new iterative method of the rational type having fifth-order of accuracy is proposed to solve initial value problems. The method is self-starting, stable, consistent, and convergent, whereas local truncation error analysis has also ...
Sania Qureshi +5 more
doaj
New, Highly Accurate Propagator for the Linear and Nonlinear Schr\"odinger Equation
, 2012 A propagation method for the time dependent Schr\"odinger equation was studied leading to a general scheme of solving ode type equations. Standard space discretization of time-dependent pde's usually results in system of ode's of the form u_t -Gu = s ...
A. Alvermanna +20 more
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A Priori Error Estimates for Mixed Finite Element $\theta$-Schemes for the Wave Equation [PDF]
, 2015 A family of implicit-in-time mixed finite element schemes is presented for the numerical approximation of the acoustic wave equation. The mixed space discretization is based on the displacement form of the wave equation and the time-stepping method ...
Karaa, Samir
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A new adaptive nonlinear numerical method for singular and stiff differential problems
Alexandria Engineering Journal, 2023 In this work, a new adaptive numerical method is proposed for solving nonlinear, singular, and stiff initial value problems often encountered in real life.
Sania Qureshi +6 more
doaj
Efficient implementation of geometric integrators for separable Hamiltonian problems
, 2013 We here investigate the efficient implementation of the energy-conserving methods named Hamiltonian Boundary Value Methods (HBVMs) recently introduced for the numerical solution of Hamiltonian problems.
Brugnano, Luigi +2 more
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