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ADVANCES IN DIFFERENCE EQUATIONS, ISSN 1687-1847, 01/2020, Volume 2020, Issue 1, pp. 1 - 12
Journal Article
BOUNDARY VALUE PROBLEMS, ISSN 1687-2770, 01/2020, Volume 2020, Issue 1, pp. 1 - 13
This research work is related to a tobacco smoking model having a significance class of users of tobacco in the form of snuffing. For this purpose, the... 
Local and global stability | MATHEMATICS | MATHEMATICS, APPLIED | Nonstandard finite difference (NSFD) scheme | EPIDEMIC MODEL | Pontryagin maximum principle | DYNAMICS | Tobacco smoking model | Control strategies | Tobacco | Maximum principle | Runge-Kutta method | Stability analysis | Control stability | Smoking | Finite difference method
Journal Article
Journal of Computational and Applied Mathematics, ISSN 0377-0427, 10/2020, Volume 376, p. 112841
In this work, we propose a new class of A-stable diagonally implicit four stage Runge–Kutta (R–K) methods with minimal dissipation and optimally low dispersion... 
Low-dissipation low-dispersion | Computational acoustics | Runge–Kutta | Diagonally implicit | Wave propagation | Time integration
Journal Article
Mathematics and Computers in Simulation, ISSN 0378-4754, 08/2020, Volume 174, pp. 59 - 75
This study proposes a class of improved Runge–Kutta–Chebyshev (RKC) methods for the stiff systems arising from the spatial discretization of partial... 
Runge–Kutta–Chebyshev methods | Explicit stabilized Runge–Kutta methods | Stiff systems | Partial differential equations
Journal Article
Applied Numerical Mathematics, ISSN 0168-9274, 07/2020, Volume 153, pp. 519 - 539
In this paper, high-order Runge-Kutta discontinuous Galerkin (RKDG) methods with multi-resolution weighted essentially non-oscillatory (WENO) limiters are... 
Multi-resolution WENO limiter | Runge-Kutta discontinuous Galerkin method | Triangular mesh | Non-oscillatory property
Journal Article
International Journal of Solids and Structures, ISSN 0020-7683, 06/2020, Volume 193-194, pp. 434 - 446
This study intends to answer how nonlinear beam theories could be rigorously derived when based on three hypotheses: Haringx/Reissner, Engesser, and Ziegler.... 
Haringx hypothesis | Shear deformation | Nonlinear beam theory | Extensibility | Runge-Kutta method | Ziegler hypothesis | Reissner formulation | Engesser hypothesis
Journal Article
Applied Mathematics Letters, ISSN 0893-9659, 06/2020, Volume 104, p. 106273
In this letter, we present two novel classes of linear high-order mass-preserving schemes for the generalized nonlinear Schrödinger equation. The original... 
Mass-preserving | Linear high-order schemes | Runge–Kutta methods | Prediction–correction | Generalized nonlinear Schrödinger equation
Journal Article
Computer Methods in Applied Mechanics and Engineering, ISSN 0045-7825, 06/2020, Volume 364, p. 112981
The phase-field crystal (PFC) equation is derived by the gradient flow for the Swift–Hohenberg free energy functional; thus, the numerical method requires the... 
High-order temporal accuracy | Unconditional energy stability | Long-time simulation | Convex Splitting Runge–Kutta method | Phase-field crystal equation
Journal Article
Applied Numerical Mathematics, ISSN 0168-9274, 06/2020, Volume 152, pp. 511 - 526
We focus our attention on the numerical simulations of compressible flows obtained by using Finite Difference in time /Finite Element in space approximation.... 
Finite element method | Explicit Runge Kutta | Stability | Optimization
Journal Article
Applied Numerical Mathematics, ISSN 0168-9274, 06/2020, Volume 152, pp. 379 - 402
Traditional explicit schemes such as the Euler-Maruyama, Milstein and stochastic Runge-Kutta methods, in general, result in strong and weak divergence when... 
Tamed stochastic Runge-Kutta method | Strong convergence | Commutative noise | Super-linearly growing coefficients | Stochastic differential equation
Journal Article
COMMUNICATIONS IN COMPUTATIONAL PHYSICS, ISSN 1815-2406, 01/2020, Volume 27, Issue 1, pp. 292 - 320
In this paper, we introduce an extension of a splitting method for singularly perturbed equations, the so-called RS-IMEX splitting [Kaiser et al., Journal of... 
low-Mach | NAVIER-STOKES EQUATIONS | RUNGE-KUTTA METHODS | HYPERBOLIC SYSTEMS | DISCONTINUOUS GALERKIN METHODS | ISENTROPIC EULER | Euler equations | FINITE-VOLUME SCHEME | PHYSICS, MATHEMATICAL | IMEX Runge-Kutta | RS-IMEX
Journal Article
Annals of Nuclear Energy, ISSN 0306-4549, 06/2020, Volume 140, p. 107100
•The coefficient averaging sub-step division is optimized by a dimensionless analysis.•An efficient two-stage method that combine CRAM and Gauss-Legendre... 
Rational approximation methods | Two-stage method | Variable coefficient | Implicit Runge-Kutta | Sub-step errors | Depletion calculation
Journal Article
International Journal of Solids and Structures, ISSN 0020-7683, 05/2020, Volume 191-192, pp. 370 - 389
Hydraulic fracture propagation is a coupled solid-fluid problem involving moving boundaries. The boundary element method is an efficient way to model it in... 
Anisotropic fracture toughness | Hydraulic fracture | Numerical simulation | Explicit time integration | Runge–Kutta–Legendre method
Journal Article
Journal of Computational Physics, ISSN 0021-9991, 05/2020, Volume 409, p. 109295
•The uniformly high order accuracy (e.g. third order) in space and in time.•Local mass conservation.•Stability under large time stepping size and unconditional... 
Implicit Runge-Kutta method | Local DG method | Stability analysis | Semi-Lagrangian | Discontinuous Galerkin (DG) method | Convection-diffusion equation
Journal Article
Journal of Computational and Applied Mathematics, ISSN 0377-0427, 05/2020, Volume 370, p. 112602
Intrusive Uncertainty Quantification methods such as stochastic Galerkin are gaining popularity, whereas the classical stochastic Galerkin approach is not... 
Uncertainty quantification | Discontinuous Galerkin | Stochastic Galerkin | Polynomial chaos | Hyperbolicity | Multi-element | MATHEMATICS, APPLIED | RUNGE-KUTTA | FLUID-FLOW | QUANTIFICATION | GENERALIZED POLYNOMIAL CHAOS | FINITE-VOLUME METHODS | COLLOCATION METHOD | PARTIAL-DIFFERENTIAL-EQUATIONS | CONSERVATION-LAWS
Journal Article
COMPUTATIONAL & APPLIED MATHEMATICS, ISSN 2238-3603, 02/2020, Volume 39, Issue 2
In this article, the authors proposed a meshfree approach for simulation of non-linear Schrodinger equation with constant and variable coefficients.... 
MULTIQUADRICS | MATHEMATICS, APPLIED | Radial basis functions | Stability | GALERKIN METHOD | DATA APPROXIMATION SCHEME | SPLINE FINITE-ELEMENT | RBF-FD TECHNIQUE | NUMERICAL-SOLUTION | Schrodinger equation | COLLOCATION | Differential quadrature method | SOLITON
Journal Article
Fuel, ISSN 0016-2361, 05/2020, Volume 267, p. 117221
[Display omitted] •Different kinetic models approaches for the transesterification were evaluated.•Particle Swarm Optimization was used to adjust the values of... 
Runge-Kutta | Rate constants | Methanolysis | Soybean oil | PSO | Self-organizing maps (SOM) | SUNFLOWER OIL | ENERGY & FUELS | ENGINEERING, CHEMICAL | CATALYZED METHANOLYSIS | PALM OIL | BIODIESEL PRODUCTION | MULTICOMPONENT DIFFUSION
Journal Article
Journal of Computational Physics, ISSN 0021-9991, 05/2020, Volume 408, p. 109238
Discontinuous Galerkin (DG) methods have become mainstays in the accurate solution of hyperbolic systems, which suggests that they should also be important for... 
Discontinuous Galerkin | von Neumann stability | Computational electrodynamics | Two-derivative Runge-Kutta | Higher order schemes | Multidimensional generalized Riemann problem solver
Journal Article
by Zhao, JJ and Zhang, YM and Xu, Y
COMPUTATIONAL & APPLIED MATHEMATICS, ISSN 2238-3603, 02/2020, Volume 39, Issue 2
A numerical method with high accuracy both in time and in space is constructed for the Riesz space fractional diffusion equation, in which the temporal... 
MATHEMATICS, APPLIED | Stability | APPROXIMATION | DIFFERENCE SCHEME | NUMERICAL-ANALYSIS | Convergence | DISCRETIZATIONS | Riesz space fractional | FINITE-VOLUME METHOD | COMPACT ADI SCHEME | Implicit Runge-Kutta method | distributed-order diffusion equation | Spectral Galerkin method
Journal Article
by Pan, KJ and Wu, XX and Yue, XQ and Ni, RX
COMPUTATIONAL & APPLIED MATHEMATICS, ISSN 2238-3603, 02/2020, Volume 39, Issue 2
In this paper, a high-order compact difference scheme is proposed for solving multidimensional nonlinear Burgers' equation. The three-stage third-order total... 
MATHEMATICS, APPLIED | Total variation diminishing | ELEMENT APPROACH | SIMULATION | FINITE-DIFFERENCE SCHEME | FLOW | ADI METHOD | Combined compact difference | NUMERICAL-SOLUTIONS | High efficiency | Burgers' equation | Sixth-order accuracy | QUADRATURE METHOD
Journal Article