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Multivalue second derivative collocation methods

Applied Numerical Mathematics, 2022
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Abdi A., Conte D., D'Ambrosio R., Paternoster B.   +3 more
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Perturbed second derivative multistep methods

Journal of Numerical Mathematics, 2015
AbstractExtended second derivative multistep methods and their modified form have been introduced as efficient numerical solvers for stiff systems. Considering these methods from second derivative general linear methods point of view, we construct some perturbations of these methods which improve their stability properties while preserve their order ...
Gholamreza Hojjati, Ali Abdi
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Second derivative methods with RK stability

Numerical Algorithms, 2005
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John C. Butcher, Gholamreza Hojjati
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Second derivative general linear methods

Numerical Algorithms, 2013
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R. I. Okuonghae, M. N. O. Ikhile
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Reanalysis Method for Second Derivatives of Static Displacement

International Journal of Computational Methods, 2019
The reanalysis method to obtain the second derivatives of static displacement is innovatively proposed in this paper. This method is based on the combined approximations method. The reanalysis formulations of the second derivative of static displacement are derived to provide a programmatic procedure of formulations construction.
Wenjie Zuo, Jiaxin Fang, Zengming Feng
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Order conditions for second derivative general linear methods

Journal of Computational and Applied Mathematics, 2021
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Afsaneh Moradi, Javad Farzi, Ali Abdi 0004   +2 more
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Second derivatives for approximate spin projection methods

The Journal of Chemical Physics, 2015
The use of broken-symmetry electronic structure methods is required in order to obtain correct behavior of electronically strained open-shell systems, such as transition states, biradicals, and transition metals. This approach often has issues with spin contamination, which can lead to significant errors in predicted energies, geometries, and ...
Lee M. Thompson, Hrant P. Hratchian
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Analytical second derivatives of the energy in MNDO methods

Journal of Computational Chemistry, 1996
Analytical second derivatives of the energy are derived and efficiently implemented for semiempirical MNDO-type methods including AM1, PM3, and MNDO/d. A new algorithm for the simultaneous solution of several CPHF equations is proposed in which the amount of memory required is independent of the number of iterations.
Serguei Patchkovskii, Walter Thiel
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A class of contractive second derivatives multistep methods

Applied Mathematics and Computation, 1989
This article studies contractivityproperties (with respect to the max- norm) of second derivative multistep methods, when they are applied to stiff differential equations. Sufficient conditions are given under which the contractivity region is closed and connected by arcs of circle.
Paula de Oliveira, F. Patricio
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Tensor Methods for Unconstrained Optimization Using Second Derivatives

SIAM Journal on Optimization, 1991
The authors discuss an unconstrained minimization algorithm in which steps are generated by augmenting the quadratic Newton model by low-rank third- and fourth- order terms. These additional tensor terms are chosen to make the model function interpolate function and derivative information at previous iterates.
Robert B. Schnabel, Ta-Tung Chow
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