BIT Numerical Mathematics, ISSN 0006-3835, 12/2016, Volume 56, Issue 4, pp. 1317 - 1337

Numerical integration of ordinary differential equations with some invariants is considered. For such a purpose, certain projection methods have proved its...

65L05 | 65L06 | Computational Mathematics and Numerical Analysis | Numeric Computing | Projection methods | Perturbed collocation methods | Mathematics, general | Mathematics | Initial value problems | Numerical geometric integration | Explicit Runge–Kutta methods | COMPUTER SCIENCE, SOFTWARE ENGINEERING | MATHEMATICS, APPLIED | NUMERICAL-SOLUTION | INTEGRATION | Explicit Runge-Kutta methods | HAMILTONIAN-SYSTEMS | Information science | Analysis | Methods

65L05 | 65L06 | Computational Mathematics and Numerical Analysis | Numeric Computing | Projection methods | Perturbed collocation methods | Mathematics, general | Mathematics | Initial value problems | Numerical geometric integration | Explicit Runge–Kutta methods | COMPUTER SCIENCE, SOFTWARE ENGINEERING | MATHEMATICS, APPLIED | NUMERICAL-SOLUTION | INTEGRATION | Explicit Runge-Kutta methods | HAMILTONIAN-SYSTEMS | Information science | Analysis | Methods

Journal Article

BIT Numerical Mathematics, ISSN 0006-3835, 9/2019, Volume 59, Issue 3, pp. 585 - 612

The theory of polar forms of polynomials is used to provide sharp bounds on the radius of the largest possible disc (absolute stability radius), and on the...

65L06 | Computational Mathematics and Numerical Analysis | Walsh’s coincidence theorem | 65L07 | Numeric Computing | Mathematics | Stability radius | Bernstein bases | Bézier curves | Mathematics, general | 65D17 | Polar forms | Explicit Runge–Kutta methods | POLYNOMIALS | COMPUTER SCIENCE, SOFTWARE ENGINEERING | MATHEMATICS, APPLIED | NUMERICAL-SOLUTION | Walsh's coincidence theorem | Explicit Runge-Kutta methods | STEP INTEGRATION METHODS | Bezier curves

65L06 | Computational Mathematics and Numerical Analysis | Walsh’s coincidence theorem | 65L07 | Numeric Computing | Mathematics | Stability radius | Bernstein bases | Bézier curves | Mathematics, general | 65D17 | Polar forms | Explicit Runge–Kutta methods | POLYNOMIALS | COMPUTER SCIENCE, SOFTWARE ENGINEERING | MATHEMATICS, APPLIED | NUMERICAL-SOLUTION | Walsh's coincidence theorem | Explicit Runge-Kutta methods | STEP INTEGRATION METHODS | Bezier curves

Journal Article

Computational Mechanics, ISSN 0178-7675, 12/2018, Volume 62, Issue 6, pp. 1429 - 1441

Diagonally implicit Runge–Kutta methods (DIRK) are evaluated and compared to standard solution procedures for finite strain crystal plasticity boundary value...

Implicit Euler | Engineering | Crystal plasticity | Numerical integration | Classical and Continuum Physics | Diagonally implicit Runge–Kutta | Theoretical and Applied Mechanics | Computational Science and Engineering | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MECHANICS | Diagonally implicit Runge-Kutta | Naturvetenskap | Computational Mathematics | Mathematics | Beräkningsmatematik | Natural Sciences | Matematik

Implicit Euler | Engineering | Crystal plasticity | Numerical integration | Classical and Continuum Physics | Diagonally implicit Runge–Kutta | Theoretical and Applied Mechanics | Computational Science and Engineering | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MECHANICS | Diagonally implicit Runge-Kutta | Naturvetenskap | Computational Mathematics | Mathematics | Beräkningsmatematik | Natural Sciences | Matematik

Journal Article

Geoscientific Model Development, ISSN 1991-959X, 04/2018, Volume 11, Issue 4, pp. 1497 - 1515

The efficient simulation of non-hydrostatic atmospheric dynamics requires time integration methods capable of overcoming the explicit stability constraints on...

ORDER | GEOSCIENCES, MULTIDISCIPLINARY | EQUATIONS | SYSTEMS | INTEGRATION METHODS | STRONG STABILITY | SCHEMES | Atmospheric circulation | Usage | Models | Mathematical models | Numerical analysis | Formulations | Sound waves | Additives | Stability | Methodology | Computer simulation | Atmospheric models | Size | Gravitational waves | Accuracy | Dynamics | Dynamic stability | Runge-Kutta method | Time integration | Nonlinear systems | Gravity waves | Gravity | Acoustic waves | GEOSCIENCES | ENVIRONMENTAL SCIENCES

ORDER | GEOSCIENCES, MULTIDISCIPLINARY | EQUATIONS | SYSTEMS | INTEGRATION METHODS | STRONG STABILITY | SCHEMES | Atmospheric circulation | Usage | Models | Mathematical models | Numerical analysis | Formulations | Sound waves | Additives | Stability | Methodology | Computer simulation | Atmospheric models | Size | Gravitational waves | Accuracy | Dynamics | Dynamic stability | Runge-Kutta method | Time integration | Nonlinear systems | Gravity waves | Gravity | Acoustic waves | GEOSCIENCES | ENVIRONMENTAL SCIENCES

Journal Article

5.
Full Text
Explicit Runge–Kutta Methods for Stiff Problems with a Gap in Their Eigenvalue Spectrum

Journal of Scientific Computing, ISSN 0885-7474, 11/2018, Volume 77, Issue 2, pp. 1055 - 1083

In this paper we consider the numerical solution of stiff problems in which the eigenvalues are separated into two clusters, one containing the “stiff”, or...

65L06 | Computational Mathematics and Numerical Analysis | 65L04 | Theoretical, Mathematical and Computational Physics | Mathematics | 65Y20 | Algorithms | Stiff problems | Mathematical and Computational Engineering | 65L20 | Exponential fitting | Explicit Runge–Kutta methods | Gap in the eigenvalue spectrum | MATHEMATICS, APPLIED | Explicit Runge-Kutta methods | STABILITY | NUMERICAL-INTEGRATION | SYSTEMS | RKC | CHEBYSHEV METHODS | S-ROCK | ORDINARY DIFFERENTIAL-EQUATIONS

65L06 | Computational Mathematics and Numerical Analysis | 65L04 | Theoretical, Mathematical and Computational Physics | Mathematics | 65Y20 | Algorithms | Stiff problems | Mathematical and Computational Engineering | 65L20 | Exponential fitting | Explicit Runge–Kutta methods | Gap in the eigenvalue spectrum | MATHEMATICS, APPLIED | Explicit Runge-Kutta methods | STABILITY | NUMERICAL-INTEGRATION | SYSTEMS | RKC | CHEBYSHEV METHODS | S-ROCK | ORDINARY DIFFERENTIAL-EQUATIONS

Journal Article

BIT Numerical Mathematics, ISSN 0006-3835, 9/2014, Volume 54, Issue 3, pp. 777 - 799

Recently, the symplectic exponentially-fitted methods for Hamiltonian systems with periodic or oscillatory solutions have been attracting a lot of interest. As...

Continuous stage Runge–Kutta method | 65L05 | Hamiltonian systems | 65L06 | Computational Mathematics and Numerical Analysis | Numeric Computing | Energy-preservation | Mathematics, general | Mathematics | Exponential fitting | OSCILLATORY DIFFERENTIAL-EQUATIONS | COMPUTER SCIENCE, SOFTWARE ENGINEERING | MATHEMATICS, APPLIED | Continuous stage Runge-Kutta method | ODES | NUMERICAL-INTEGRATION | MANIFOLDS | GAUSS TYPE | SCHEMES

Continuous stage Runge–Kutta method | 65L05 | Hamiltonian systems | 65L06 | Computational Mathematics and Numerical Analysis | Numeric Computing | Energy-preservation | Mathematics, general | Mathematics | Exponential fitting | OSCILLATORY DIFFERENTIAL-EQUATIONS | COMPUTER SCIENCE, SOFTWARE ENGINEERING | MATHEMATICS, APPLIED | Continuous stage Runge-Kutta method | ODES | NUMERICAL-INTEGRATION | MANIFOLDS | GAUSS TYPE | SCHEMES

Journal Article

Journal of Scientific Computing, ISSN 0885-7474, 1/2016, Volume 66, Issue 1, pp. 177 - 195

To integrate large systems of locally coupled ordinary differential equations with disparate timescales, we present a multirate method with error control that...

Interpolation | Computational Mathematics and Numerical Analysis | Runge–Kutta | Algorithms | Theoretical, Mathematical and Computational Physics | Appl.Mathematics/Computational Methods of Engineering | Multirate | Mathematics | MATHEMATICS, APPLIED | STIFF ODES | TIME INTEGRATION | Runge-Kutta | CONSERVATION-LAWS | FORMULAS | ORDINARY DIFFERENTIAL-EQUATIONS | Errors | Mathematical analysis | Differential equations | Control systems | Joining | Polynomials | Runge-Kutta method | Convergence

Interpolation | Computational Mathematics and Numerical Analysis | Runge–Kutta | Algorithms | Theoretical, Mathematical and Computational Physics | Appl.Mathematics/Computational Methods of Engineering | Multirate | Mathematics | MATHEMATICS, APPLIED | STIFF ODES | TIME INTEGRATION | Runge-Kutta | CONSERVATION-LAWS | FORMULAS | ORDINARY DIFFERENTIAL-EQUATIONS | Errors | Mathematical analysis | Differential equations | Control systems | Joining | Polynomials | Runge-Kutta method | Convergence

Journal Article

Applied Mathematical Modelling, ISSN 0307-904X, 12/2012, Volume 36, Issue 12, pp. 6331 - 6337

For the general multidimensional oscillatory systems y″+Ky=f(y,y′) with K∈Rd×d, a positive semi-definite matrix, the order conditions for the ARKN methods are...

Oscillatory systems | Stability analysis | Adapted Runge–Kutta–Nyström methods | Multidimensional ARKN methods | Adapted Runge-Kutta-Nyström methods | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MECHANICS | ENGINEERING, MULTIDISCIPLINARY | Adapted Runge-Kutta-Nystrom methods | NUMERICAL-INTEGRATION | EXPLICIT ARKN METHODS | PERTURBED OSCILLATORS | PAIR

Oscillatory systems | Stability analysis | Adapted Runge–Kutta–Nyström methods | Multidimensional ARKN methods | Adapted Runge-Kutta-Nyström methods | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MECHANICS | ENGINEERING, MULTIDISCIPLINARY | Adapted Runge-Kutta-Nystrom methods | NUMERICAL-INTEGRATION | EXPLICIT ARKN METHODS | PERTURBED OSCILLATORS | PAIR

Journal Article

International Journal for Numerical Methods in Fluids, ISSN 0271-2091, 10/2016, Volume 82, Issue 4, pp. 218 - 227

Summary A hybrid time stepping scheme is developed and implemented by a combination of explicit Runge–Kutta with implicit LU‐SGS scheme at the level of system...

Navier–Stokes equations | time integration | aerodynamics | hybrid time stepping scheme | implicit–explicit (IMEX) method | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MECHANICS | PHYSICS, FLUIDS & PLASMAS | implicit-explicit (IMEX) method | Navier-Stokes equations | Operators | Turbulence | Computational fluid dynamics | Mathematical analysis | Fluid flow | Mathematical models | Runge-Kutta method

Navier–Stokes equations | time integration | aerodynamics | hybrid time stepping scheme | implicit–explicit (IMEX) method | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MECHANICS | PHYSICS, FLUIDS & PLASMAS | implicit-explicit (IMEX) method | Navier-Stokes equations | Operators | Turbulence | Computational fluid dynamics | Mathematical analysis | Fluid flow | Mathematical models | Runge-Kutta method

Journal Article

Numerical Algorithms, ISSN 1017-1398, 9/2015, Volume 70, Issue 1, pp. 133 - 150

The paper presents a trigonometrically-fitted implicit third derivative Runge-Kutta-Nystöm method (TTRKNM) whose coefficients depend on the frequency and...

65L05 | 65L06 | Runge-Kutta-Nystöm method | Algorithms | Algebra | Trigonometrically-fitted | Numerical Analysis | Computer Science | Numeric Computing | Third derivative | Oscillatory initial value problems | Theory of Computation | FITTED METHODS | MATHEMATICS, APPLIED | 2-STEP METHODS | INITIAL-VALUE PROBLEMS | COLLOCATION METHODS | MULTISTEP METHODS | F(X | NUMERICAL-INTEGRATION | Y | Runge-Kutta-Nystom method | EXPLICIT | F X

65L05 | 65L06 | Runge-Kutta-Nystöm method | Algorithms | Algebra | Trigonometrically-fitted | Numerical Analysis | Computer Science | Numeric Computing | Third derivative | Oscillatory initial value problems | Theory of Computation | FITTED METHODS | MATHEMATICS, APPLIED | 2-STEP METHODS | INITIAL-VALUE PROBLEMS | COLLOCATION METHODS | MULTISTEP METHODS | F(X | NUMERICAL-INTEGRATION | Y | Runge-Kutta-Nystom method | EXPLICIT | F X

Journal Article

Advances in Computational Mathematics, ISSN 1019-7168, 2/2015, Volume 41, Issue 1, pp. 231 - 251

In this paper new one-step methods that combine Runge–Kutta (RK) formulae with a suitable projection after the step are proposed for the numerical solution of...

65L05 | Visualization | 65L06 | Computational Mathematics and Numerical Analysis | Mathematical and Computational Biology | Projection methods | Mathematics | Computational Science and Engineering | Dispersion error | Initial value problems | Mathematical Modeling and Industrial Mathematics | Numerical geometric integration | Explicit Runge–Kutta methods | PRESERVE | MATHEMATICS, APPLIED | RIGID-BODY | INVARIANTS | Explicit Runge-Kutta methods | ODES | OSCILLATING SOLUTIONS | GEOMETRIC INTEGRATION | Boundary value problems | Numerical analysis | Research | Integrals | Mathematical research

65L05 | Visualization | 65L06 | Computational Mathematics and Numerical Analysis | Mathematical and Computational Biology | Projection methods | Mathematics | Computational Science and Engineering | Dispersion error | Initial value problems | Mathematical Modeling and Industrial Mathematics | Numerical geometric integration | Explicit Runge–Kutta methods | PRESERVE | MATHEMATICS, APPLIED | RIGID-BODY | INVARIANTS | Explicit Runge-Kutta methods | ODES | OSCILLATING SOLUTIONS | GEOMETRIC INTEGRATION | Boundary value problems | Numerical analysis | Research | Integrals | Mathematical research

Journal Article

Journal of Mathematical Chemistry, ISSN 0259-9791, 1/2017, Volume 55, Issue 1, pp. 259 - 277

A new family of one-parameter equation dependent Runge–Kutta–Nyström (EDRKN) methods for the numerical solution of second–order differential equations are...

65L05 | Theoretical and Computational Chemistry | 65L06 | Chemistry | Equation dependent coefficient | Physical Chemistry | Dissipation | Oscillatory problems | Math. Applications in Chemistry | Dispersion | ERRORS | INITIAL-VALUE-PROBLEMS | SCHRODINGER-EQUATION | ALGORITHMS | CHEMISTRY, MULTIDISCIPLINARY | TRIGONOMETRICALLY-FITTED METHODS | CHOICE | NUMERICAL-SOLUTION | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | INTEGRATION | FREQUENCY | EXPLICIT | Analysis | Differential equations

65L05 | Theoretical and Computational Chemistry | 65L06 | Chemistry | Equation dependent coefficient | Physical Chemistry | Dissipation | Oscillatory problems | Math. Applications in Chemistry | Dispersion | ERRORS | INITIAL-VALUE-PROBLEMS | SCHRODINGER-EQUATION | ALGORITHMS | CHEMISTRY, MULTIDISCIPLINARY | TRIGONOMETRICALLY-FITTED METHODS | CHOICE | NUMERICAL-SOLUTION | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | INTEGRATION | FREQUENCY | EXPLICIT | Analysis | Differential equations

Journal Article

SIAM Journal on Numerical Analysis, ISSN 0036-1429, 1/2013, Volume 51, Issue 4, pp. 2149 - 2165

We apply the concept of effective order to strong stability preserving (SSP) explicit Runge-Kutta methods. Relative to classical Runge-Kutta methods, methods...

Mathematical problems | Algebra | Mathematical monotonicity | Business orders | Matrices | Runge Kutta method | Coefficients | Butchering | Order of integration | Strong stability preserving (SSP) | Runge-Kutta methods | High-order accuracy | Time integration | Effective order | Monotonicity | MATHEMATICS, APPLIED | effective order | time integration | high-order accuracy | strong stability preserving (SSP) | monotonicity | CONTRACTIVITY | Construction | Accuracy | Numerical analysis | Stability | Mathematical models | Preserving | Optimization | Mathematics - Numerical Analysis

Mathematical problems | Algebra | Mathematical monotonicity | Business orders | Matrices | Runge Kutta method | Coefficients | Butchering | Order of integration | Strong stability preserving (SSP) | Runge-Kutta methods | High-order accuracy | Time integration | Effective order | Monotonicity | MATHEMATICS, APPLIED | effective order | time integration | high-order accuracy | strong stability preserving (SSP) | monotonicity | CONTRACTIVITY | Construction | Accuracy | Numerical analysis | Stability | Mathematical models | Preserving | Optimization | Mathematics - Numerical Analysis

Journal Article

SIAM Journal on Scientific Computing, ISSN 1064-8275, 2011, Volume 33, Issue 4, pp. 1707 - 1725

An integration method based on Runge-Kutta-Chebyshev (RKC) methods is discussed which has been designed to treat moderately stiff and nonstiff terms...

Numerical integration of differential equations | Stabilized second-order integration method | Partitioned Runge-Kutta methods | Runge-Kutta-Chebyshev methods | MATHEMATICS, APPLIED | numerical integration of differential equations | PARABOLIC EQUATIONS | INTEGRATION | PDES | RKC | SOLVER | stabilized second-order integration method | EXPLICIT | partitioned Runge-Kutta methods

Numerical integration of differential equations | Stabilized second-order integration method | Partitioned Runge-Kutta methods | Runge-Kutta-Chebyshev methods | MATHEMATICS, APPLIED | numerical integration of differential equations | PARABOLIC EQUATIONS | INTEGRATION | PDES | RKC | SOLVER | stabilized second-order integration method | EXPLICIT | partitioned Runge-Kutta methods

Journal Article

Numerical Algorithms, ISSN 1017-1398, 12/2016, Volume 73, Issue 4, pp. 1037 - 1054

In this paper we study efficient iterative methods for solving the system of linear equations arising from the fully implicit Runge-Kutta discretizations of a...

65L06 | Numeric Computing | Theory of Computation | Implicit Runge-Kutta methods | Differential-algebraic equation | Bidomain equations | Algorithms | Algebra | 65F10 | Numerical Analysis | Computer Science | Iterative methods | Preconditioning | 65N22 | BLOCK-TRIANGULAR PRECONDITIONER | LINEAR-SYSTEMS | MATHEMATICS, APPLIED | SADDLE-POINT PROBLEMS | MODEL | BOUNDARY-VALUE METHODS | RUSH-LARSEN METHOD | SCHWARZ | ELECTROCARDIOLOGY | Differential equations | Linear systems | Splitting | Discretization | Mathematical analysis | Strategy | Runge-Kutta method | Spectra | Time integration

65L06 | Numeric Computing | Theory of Computation | Implicit Runge-Kutta methods | Differential-algebraic equation | Bidomain equations | Algorithms | Algebra | 65F10 | Numerical Analysis | Computer Science | Iterative methods | Preconditioning | 65N22 | BLOCK-TRIANGULAR PRECONDITIONER | LINEAR-SYSTEMS | MATHEMATICS, APPLIED | SADDLE-POINT PROBLEMS | MODEL | BOUNDARY-VALUE METHODS | RUSH-LARSEN METHOD | SCHWARZ | ELECTROCARDIOLOGY | Differential equations | Linear systems | Splitting | Discretization | Mathematical analysis | Strategy | Runge-Kutta method | Spectra | Time integration

Journal Article

The Journal of the Astronautical Sciences, ISSN 0021-9142, 12/2017, Volume 64, Issue 4, pp. 333 - 360

A variable-step Gauss-Legendre implicit Runge-Kutta (GLIRK) propagator is applied to coupled orbit/attitude propagation. Concepts previously shown to improve...

Engineering | Parallel computing | Propagation | Six degrees of freedom | Attitude | Space Sciences (including Extraterrestrial Physics, Space Exploration and Astronautics) | Implicit Runge-Kutta | Mathematical Applications in the Physical Sciences | Aerospace Technology and Astronautics | ITERATION | UNCERTAINTY PROPAGATION | IMPLEMENTATION | DIFFERENTIAL-EQUATIONS | ENGINEERING, AEROSPACE | ORBIT PROPAGATION | MOTION | DYNAMICS | NUMERICAL-INTEGRATION

Engineering | Parallel computing | Propagation | Six degrees of freedom | Attitude | Space Sciences (including Extraterrestrial Physics, Space Exploration and Astronautics) | Implicit Runge-Kutta | Mathematical Applications in the Physical Sciences | Aerospace Technology and Astronautics | ITERATION | UNCERTAINTY PROPAGATION | IMPLEMENTATION | DIFFERENTIAL-EQUATIONS | ENGINEERING, AEROSPACE | ORBIT PROPAGATION | MOTION | DYNAMICS | NUMERICAL-INTEGRATION

Journal Article

Nonlinear Dynamics, ISSN 0924-090X, 7/2015, Volume 81, Issue 1, pp. 169 - 188

A typical two-dimensional airfoil with freeplay nonlinearity in pitch undergoing subsonic flow is studied via numerical integration methods. Due to the...

Engineering | Vibration, Dynamical Systems, Control | Freeplay nonlinearity | Henon’s method | Mechanics | Automotive Engineering | Chaotic transient | Mechanical Engineering | Largest Lyapunov exponent | Rational polynomial approximation | Discontinuity | Numerical integration | Stability | Computer simulation | Subsonic flow | Numerical methods | Nonlinearity | Runge-Kutta method | Polynomials | Aeroelasticity | Methods | Subsonic aircraft

Engineering | Vibration, Dynamical Systems, Control | Freeplay nonlinearity | Henon’s method | Mechanics | Automotive Engineering | Chaotic transient | Mechanical Engineering | Largest Lyapunov exponent | Rational polynomial approximation | Discontinuity | Numerical integration | Stability | Computer simulation | Subsonic flow | Numerical methods | Nonlinearity | Runge-Kutta method | Polynomials | Aeroelasticity | Methods | Subsonic aircraft

Journal Article

Computational and Mathematical Methods in Medicine, ISSN 1748-670X, 10/2015, Volume 2015, pp. 689137 - 14

Oscillation is one of the most important phenomena in the chemical reaction systems in living cells. The general purpose simulation algorithms fail to take...

DROSOPHILA PERIOD PROTEIN | FREQUENCY EVALUATION | MATHEMATICAL & COMPUTATIONAL BIOLOGY | NUMERICAL-INTEGRATION | CELL-CYCLE | MODEL | INITIAL-VALUE PROBLEMS | Computational Biology - methods | Algorithms | Animals | Period Circadian Proteins - genetics | Computer Simulation | Models, Genetic | Drosophila Proteins - genetics | Gene Regulatory Networks | Drosophila - genetics | Genetic research | Analysis | Drosophila | Methods

DROSOPHILA PERIOD PROTEIN | FREQUENCY EVALUATION | MATHEMATICAL & COMPUTATIONAL BIOLOGY | NUMERICAL-INTEGRATION | CELL-CYCLE | MODEL | INITIAL-VALUE PROBLEMS | Computational Biology - methods | Algorithms | Animals | Period Circadian Proteins - genetics | Computer Simulation | Models, Genetic | Drosophila Proteins - genetics | Gene Regulatory Networks | Drosophila - genetics | Genetic research | Analysis | Drosophila | Methods

Journal Article

Computational Optimization and Applications, ISSN 0926-6003, 1/2007, Volume 36, Issue 1, pp. 83 - 108

This paper considers the numerical solution of optimal control problems based on ODEs. We assume that an explicit Runge-Kutta method is applied to integrate...

Adjoint equation | Sensitivity equation | Convex and Discrete Geometry | Operations Research/Decision Theory | Optimal control | Mathematics | Operations Research, Mathematical Programming | Statistics, general | Optimization | Automatic differentiation | MATHEMATICS, APPLIED | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | adjoint equation | automatic differentiation | optimal control | GRADIENTS | sensitivity equation | Studies | Integration | Methods | Convergence

Adjoint equation | Sensitivity equation | Convex and Discrete Geometry | Operations Research/Decision Theory | Optimal control | Mathematics | Operations Research, Mathematical Programming | Statistics, general | Optimization | Automatic differentiation | MATHEMATICS, APPLIED | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | adjoint equation | automatic differentiation | optimal control | GRADIENTS | sensitivity equation | Studies | Integration | Methods | Convergence

Journal Article

Computer Methods in Applied Mechanics and Engineering, ISSN 0045-7825, 03/2020, Volume 360, p. 112772

Nowadays mathematical models and numerical simulations are widely used in the field of hemodynamics, representing a valuable resource to better understand...

Blood flow equations | Viscoelastic effects | Fluid–structure interaction | Compliant vessels | IMEX Runge–Kutta schemes | Finite volume methods | NUMERICAL-METHODS | CARDIOVASCULAR-SYSTEM | 1-D | VALIDATION | Fluid-structure interaction | HEMODYNAMICS | HUMAN ARTERIAL NETWORK | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MECHANICS | ENGINEERING, MULTIDISCIPLINARY | PULSE-WAVE PROPAGATION | SIMULATIONS | HYPERBOLIC CONSERVATION-LAWS | IMEX Runge-Kutta schemes | VERIFICATION | Viscoelasticity | Pressure effects | Computational fluid dynamics | Computer simulation | Rheology | Fluid flow | Exact solutions | Blood vessels | Modulus of elasticity | Elastic waves | Blood flow | Viscous damping | Strain | Incompressible flow | Robustness (mathematics) | Tubes | Mathematical models | Runge-Kutta method | Hemodynamics | Time integration | Hyperbolic systems | Rheological properties

Blood flow equations | Viscoelastic effects | Fluid–structure interaction | Compliant vessels | IMEX Runge–Kutta schemes | Finite volume methods | NUMERICAL-METHODS | CARDIOVASCULAR-SYSTEM | 1-D | VALIDATION | Fluid-structure interaction | HEMODYNAMICS | HUMAN ARTERIAL NETWORK | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MECHANICS | ENGINEERING, MULTIDISCIPLINARY | PULSE-WAVE PROPAGATION | SIMULATIONS | HYPERBOLIC CONSERVATION-LAWS | IMEX Runge-Kutta schemes | VERIFICATION | Viscoelasticity | Pressure effects | Computational fluid dynamics | Computer simulation | Rheology | Fluid flow | Exact solutions | Blood vessels | Modulus of elasticity | Elastic waves | Blood flow | Viscous damping | Strain | Incompressible flow | Robustness (mathematics) | Tubes | Mathematical models | Runge-Kutta method | Hemodynamics | Time integration | Hyperbolic systems | Rheological properties

Journal Article