Nonstandard finite differences numerical methods for a vegetation reaction–diffusion model

D Conte, G Pagano, B Paternoster - Journal of Computational and Applied …, 2023 - Elsevier
In this work we derive NonStandard Finite Differences (NSFDs)(Anguelov and Lubuma,
2001; Mickens, 2020) numerical schemes to solve a model consisting of reaction–diffusion …

[HTML][HTML] Time-accurate and highly-stable explicit peer methods for stiff differential problems

D Conte, G Pagano, B Paternoster - Communications in Nonlinear Science …, 2023 - Elsevier
We derive a new class of parallelizable two-step peer methods for the numerical solution of
stiff systems of Ordinary Differential Equations (ODEs), inspired by a technique introduced in …

Exponentially fitted two-step peer methods for oscillatory problems

D Conte, F Mohammadi, L Moradi… - … and Applied Mathematics, 2020 - Springer
This paper concerns the construction of a general class of exponentially fitted two-step
implicit peer methods for the numerical integration of Ordinary Differential Equations (ODEs) …

Two-step peer methods with equation-dependent coefficients

D Conte, G Pagano, B Paternoster - Computational and Applied …, 2022 - Springer
We introduce a new class of explicit two-step peer methods with the aim of improving the
stability properties of already existing peer methods, by making use of coefficients …

Multivalue mixed collocation methods

D Conte, R D'Ambrosio, MP D'Arienzo… - Applied Mathematics and …, 2021 - Elsevier
This paper is devoted to the construction of multivalue mixed collocation methods suitable
for ordinary differential systems whose solution is known in advance to be oscillatory …

On the advantages of nonstandard finite difference discretizations for differential problems

D Conte, N Guarino, G Pagano… - Numerical Analysis and …, 2022 - Springer
The goal of this work is to highlight the advantages of using NonStandard Finite Difference
(NSFD) numerical schemes for the solution of ordinary differential equations (ODEs) and …

Exponentially fitted methods that preserve conservation laws

D Conte, G Frasca-Caccia - Communications in Nonlinear Science and …, 2022 - Elsevier
The exponential fitting technique uses information on the expected behaviour of the solution
of ordinary and partial differential equations to define accurate and efficient numerical …

A numerical scheme based on the collocation and optimization methods for accurate solution of sensitive boundary value problems

MA Mehrpouya, R Salehi - The European Physical Journal Plus, 2021 - Springer
Despite the significant advances in the numerical solution of nonlinear boundary value
problems, most of the existing methods still encounter with a high sensitivity to the initial …

Jacobian-dependent vs Jacobian-free discretizations for nonlinear differential problems

D Conte, R D'Ambrosio, G Pagano… - … and Applied Mathematics, 2020 - Springer
The paper provides a comparison between two relevant classes of numerical discretizations
for stiff and nonstiff problems. Such a comparison regards linearly implicit Jacobian …

Construction of exponentially fitted explicit peer methods

D Conte, B Paternoster, L Moradi… - International Journal of …, 2019 - elibrary.ru
It is the purpose of this work to present exponentially fitted explicit two-step peer methods for
the numerical integration of ordinary differential equations exhibiting oscillatory solution. We …