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Mediterranean Journal of Mathematics, ISSN 1660-5446, 08/2016, Volume 13, Issue 4, pp. 2271 - 2285
In this work, we give the general framework for constructing trigonometrically fitted symplectic Runge-Kutta-Nystrom (RKN) methods from symplectic... 
65L05 | Runge-Kutta-Nystrom methods | MATHEMATICS | Hamiltonian systems | MATHEMATICS, APPLIED | FREQUENCY EVALUATION | Partitioned Runge-Kutta methods | ODES | NUMERICAL-INTEGRATION | symplectic methods | trigonometrical fitting | OSCILLATING SOLUTIONS | INITIAL-VALUE PROBLEMS | Computer science | International trade | Methods | Resveratrol
Journal Article
01/2019, ISBN 3038976679
The use of scientific computing tools is currently customary for solving problems at several complexity levels in Applied Sciences. The great need for reliable... 
structured matrices | curl | numerical methods | time fractional differential equations | hierarchical splines | finite difference methods | null-space | highly oscillatory problems | stochastic Volterra integral equations | differential equations | displacement rank | constrained Hamiltonian problems | Hermite | hyperbolic partial differential equations | higher-order finite element methods | continuous geometric average | Volterra integro | spectral (eigenvalue) and singular value distributions | generalized locally Toeplitz sequences | Obreshkov methods | B-spline | discontinuous Galerkin methods | adaptive methods | Cholesky factorization | energy-conserving methods | order | collocation method | Poisson problems | time harmonic Maxwell’s equations and magnetostatic problems | tree | multistep methods | stochastic differential equations | optimal basis | finite difference method | elementary differential | gradient system | Runge | conservative problems | line integral methods | stochastic multistep methods | Hamiltonian Boundary Value Methods | Kutta | limited memory | boundary element method | convergence | analytical solution | preconditioners | asymptotic stability | collocation methods | histogram specification | local refinement | edge-preserving smoothing | numerical analysis | THB-splines | BS methods | barrier options | stump | shock waves and discontinuities | mean-square stability | Volterra integral equations | high order discontinuous Galerkin finite element schemes | B-splines | vectorization and parallelization | initial value problems | one-step methods | scientific computing | fractional derivative | linear systems | Hamiltonian problems | low rank completion | ordinary differential equations | mixed-index problems | edge-histogram | Hamiltonian PDEs | matrix ODEs | HBVMs | floating strike Asian options | generalized Schur algorithm | Galerkin method | symplecticity | high performance computing | isogeometric analysis | discretization of systems of differential equations | curl operator
eBook
Applied Mathematics and Computation, ISSN 0096-3003, 12/2018, Volume 339, pp. 231 - 241
We provide a note on continuous-stage Runge–Kutta methods (csRK) for solving initial value problems of first-order ordinary differential equations. Such... 
Symplectic methods | Hamiltonian systems | Symmetric methods | Energy-preserving methods | Continuous-stage Runge–Kutta methods | Conjugate-symplectic methods | MATHEMATICS, APPLIED | Continuous-stage Runge-Kutta methods | HAMILTONIAN-SYSTEMS | CONSTRUCTION | ODES | FRAMEWORK | INTEGRATORS | Analysis | Methods | Differential equations
Journal Article
Journal of Computational Physics, ISSN 0021-9991, 10/2018, Volume 371, pp. 168 - 191
Journal Article
Applied Mathematics and Computation, ISSN 0096-3003, 04/2018, Volume 323, pp. 204 - 219
In this paper, we develop continuous-stage Runge–Kutta–Nyström (csRKN) methods for numerical integration of second-order ordinary differential equations (ODEs)... 
Symplecticity-preserving | Hamiltonian systems | Continuous-stage Runge–Kutta–Nyström methods | Symplectic conditions | Legendre polynomial | MATHEMATICS, APPLIED | Continuous-stage Runge-Kutta-Nystrom | methods | HAMILTONIAN-SYSTEMS | CONSTRUCTION | ODES
Journal Article
Computers and Fluids, ISSN 0045-7930, 12/2017, Volume 159, pp. 156 - 166
•A new method for the numerical solution of ODEs is presented.•Approach is based on an approximate formulation of Taylor methods.•Functions, and not... 
Taylor methods | Faà di Bruno’s formula | ODE integrators | Faà di Bruno's formula | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | MECHANICS | Faa di Bruno's formula | SCHEMES | Derivatives (Financial instruments) | Methods
Journal Article
Journal of Computational and Applied Mathematics, ISSN 0377-0427, 03/2018, Volume 330, pp. 618 - 629
The purpose of this paper is the derivation of symmetric second derivative general linear methods (SGLMs) for general time-reversible differential equations.... 
Hamiltonian systems | Symmetric methods | Reversible problems | G-symplecticity | General linear methods | Second derivative methods | HAMILTONIAN PROBLEMS | MATHEMATICS, APPLIED | RUNGE-KUTTA METHODS | STABILITY | ORDER | STIFF ODES | MULTISTEP METHODS | G-SYMPLECTIC METHODS | NUMERICAL-INTEGRATION | ORDINARY DIFFERENTIAL-EQUATIONS
Journal Article
Journal of Computational Physics, ISSN 0021-9991, 12/2016, Volume 326, pp. 141 - 155
Journal Article
SIAM Journal on Numerical Analysis, ISSN 0036-1429, 2017, Volume 55, Issue 5, pp. 2255 - 2285
Journal Article
Journal of Computational and Applied Mathematics, ISSN 0377-0427, 06/2011, Volume 235, Issue 16, pp. 4888 - 4897
It is the purpose of this paper to derive two-step hybrid methods for y″=f(x,y), with oscillatory or periodic solutions, specially tuned to the behaviour of... 
Exponential fitting | Second order ordinary differential equations | Two-step hybrid methods | MATHEMATICS, APPLIED | Y''=F(X,Y) | SCHRODINGER-EQUATION | ODES | FITTING METHODS | COLLOCATION METHODS | ORDER | ORDINARY DIFFERENTIAL EQUATIONS | NUMERICAL-SOLUTION | KUTTA-NYSTROM METHODS | P-STABILITY | Construction | Fittings | Mathematical models | Computation
Journal Article
Applied Numerical Mathematics, ISSN 0168-9274, 09/2017, Volume 119, pp. 164 - 178
In this paper we discuss the efficient implementation of RKN-type Fourier collocation methods, which are used when solving second-order differential equations.... 
Second-order differential equations | Implementation | RKN-type Fourier collocation methods | Blended implicit methods | MATHEMATICS, APPLIED | ODES | STEP METHODS | IMPLICIT METHODS | INITIAL-VALUE PROBLEMS | BOUNDARY-VALUE METHODS | NUMERICAL-SOLUTION | KUTTA-NYSTROM METHODS | SYSTEMS | Analysis | Methods | Differential equations
Journal Article
Applied Numerical Mathematics, ISSN 0168-9274, 04/2020, Volume 150, Issue C, pp. 233 - 251
Many scientific applications require the solution of large initial-value problems, such as those produced by the method of lines after semi-discretization in... 
PDE | ODE | Krylov | Biorthogonal Lanczos | Time integration | Rosenbrock
Journal Article
Applied Mathematics Letters, ISSN 0893-9659, 04/2014, Volume 30, pp. 56 - 60
Journal Article
Computers and Fluids, ISSN 0045-7930, 06/2018, Volume 169, pp. 87 - 97
•A new method for the numerical solution of ODEs is presented.•Approach is based on an approximate formulation of Taylor methods.•Functions, and not... 
Taylor methods | Faà di Bruno’s formula | ODE integrators | Faà di Bruno's formula | Derivatives (Financial instruments) | Methods
Journal Article
Applied Mathematics and Computation, ISSN 0096-3003, 04/2019, Volume 347, pp. 354 - 359
We present an approach to the factorization method for second order difference equations on time scales. We construct Hilbert spaces of functions on the time... 
Ladder operators | Difference equations | Time scales | Factorization method | MATHEMATICS, APPLIED | HYPERGEOMETRIC TYPE | DIFFERENCE-EQUATIONS | OPERATORS | Mathematics - General Topology
Journal Article
Methods in Molecular Biology, ISSN 1064-3745, 2016, Volume 1333, pp. 207 - 240
Bacterial persister cells are dormant cells, tolerant to multiple antibiotics, that are involved in several chronic infections. Toxin-antitoxin modules play a... 
ODE | Toxin-antitoxin | Gillespie | Persister | Stochastic | Modeling | Biofilms - drug effects | Anti-Bacterial Agents - therapeutic use | Bacteria - growth & development | Computational Biology - methods | Humans | Bacteria - drug effects | Biofilms - growth & development | Drug Resistance, Bacterial - genetics
Journal Article