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Nonstandard finite differences numerical methods for a vegetation reaction–diffusion model
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 …
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
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 …
stiff systems of Ordinary Differential Equations (ODEs), inspired by a technique introduced in …
Exponentially fitted two-step peer methods for oscillatory problems
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) …
implicit peer methods for the numerical integration of Ordinary Differential Equations (ODEs) …
Two-step peer methods with equation-dependent coefficients
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 …
stability properties of already existing peer methods, by making use of coefficients …
Multivalue mixed collocation methods
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 …
for ordinary differential systems whose solution is known in advance to be oscillatory …
On the advantages of nonstandard finite difference discretizations for differential problems
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 …
(NSFD) numerical schemes for the solution of ordinary differential equations (ODEs) and …
Exponentially fitted methods that preserve conservation laws
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 …
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
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 …
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
The paper provides a comparison between two relevant classes of numerical discretizations
for stiff and nonstiff problems. Such a comparison regards linearly implicit Jacobian …
for stiff and nonstiff problems. Such a comparison regards linearly implicit Jacobian …
Construction of exponentially fitted explicit peer methods
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 …
the numerical integration of ordinary differential equations exhibiting oscillatory solution. We …