Exploiting structure in the construction of DIMSIMs
, 1997 . We describe the structure of the nonlinear system for the coefficients of diagonally implicit multistage integration methods for ordinary differential equations.
H. D. Mittelmann, Z. Jackiewicz
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Multiresolutional Methods for Difference Equations
, 1994 . We develop a stable direct method with linear complexity for solving large banded sparse linear systems which are typical for the finite difference discretization of one-dimensional differential equations.
Wei-Chang Shann, I-Liang Chern
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Enforcing Dirichlet boundary conditions in physics-informed neural networks and variational physics-informed neural networks. [PDF]
Heliyon, 2023 Berrone S +3 more
europepmc +1 more source
Exponentially fitted numerical method for solving singularly perturbed delay reaction-diffusion problem with nonlocal boundary condition. [PDF]
BMC Res Notes, 2023 Wondimu GM +3 more
europepmc +1 more source
Stable Spectral Methods For Conservation Laws On Triangles With Unstructured Grids
, 1997 . This paper presents an asymptotically stable scheme for the spectral approximation of linear conservation laws defined on a triangle. Lagrange interpolation on a general two-dimensional nodal set is employed and, by imposing the boundary conditions ...
D. Gottlieb, J. S. Hesthaven
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On the Construction of Stiffly Accurate and B-Stable Runge-Kutta Methods
, 1996 . In the solution of stiff ODEs and especially DAEs it is desirable that the method used is stiffly accurate and B-stable. In this paper guidelines for the construction of Runge-Kutta methods with these properties are presented.
Claus Bendtsen
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On Roots And Error Constants Of Optimal Stability Polynomials.
, 1998 . Optimal stability polynomials are polynomials whose stability region is as large as possible in a certain region, here the real-negative axis. We are interested in such polynomials wich in addition, obey a certain order condition.
Assyr Abdulle
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Efficient simulation of a slow-fast dynamical system using multirate finite difference schemes
, 2016 We consider a system of ordinary differential equations describing a slow-fast dynamical system, in particular, a predator-prey system that is highly susceptible to local time variations.
Patidar, Kailash C., Mergia, Woinshet D.
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Global stability analysis of the role of multi-therapies and non-pharmaceutical treatment protocols for COVID-19 pandemic. [PDF]
Chaos Solitons Fractals, 2021 Bassey BE, Atsu JU.
europepmc +1 more source
Nonlinear Optimization Approach to Construction of General Linear Methods of High Order
. We describe the construction of diagonally implicit multistage integration methods of order and stage order p = q = 7 and p = q = 8 for ordinary differential equations.
Butcher Jackiewicz And +2 more
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