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Numerical Analysis or Numerical Method in Symmetry

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ISBN: 9783039283729 9783039283736 Year: Pages: 194 DOI: 10.3390/books978-3-03928-373-6 Language: English
Publisher: MDPI - Multidisciplinary Digital Publishing Institute
Subject: Science (General) --- Mathematics
Added to DOAB on : 2020-04-07 23:07:08
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Abstract

This Special Issue focuses mainly on techniques and the relative formalism typical of numerical methods and therefore of numerical analysis, more generally. These fields of study of mathematics represent an important field of investigation both in the field of applied mathematics and even more exquisitely in the pure research of the theory of approximation and the study of polynomial relations as well as in the analysis of the solutions of the differential equations both ordinary and partial derivatives. Therefore, a substantial part of research on the topic of numerical analysis cannot exclude the fundamental role played by approximation theory and some of the tools used to develop this research. In this Special Issue, we want to draw attention to the mathematical methods used in numerical analysis, such as special functions, orthogonal polynomials, and their theoretical tools, such as Lie algebra, to study the concepts and properties of some special and advanced methods, which are useful in the description of solutions of linear and nonlinear differential equations. A further field of investigation is dedicated to the theory and related properties of fractional calculus with its adequate application to numerical methods.

Keywords

risk assessment --- numerical analysis --- ignition hazard --- effective field strength --- offshore plant --- Hamiltonian system --- complex Lagrangian --- Noether symmetries --- first integrals --- symplectic Runge–Kutta methods --- effective order --- partitioned runge-kutta methods --- symplecticity --- hamiltonian systems --- Runge-Kutta type methods --- fourth-order ODEs --- order conditions --- B-series --- quad-colored trees --- k-hypergeometric differential equations --- non-homogeneous --- k-hypergeometric series --- special function --- general solution --- Frobenius method --- Chebyshev polynomials --- pseudo-Chebyshev polynomials --- recurrence relations --- differential equations --- composition properties --- orthogonality properties --- numerical analysis --- heat generation --- chemical reaction --- thin needle --- nanofluid --- fourth-order --- nonoscillatory solutions --- oscillatory solutions --- delay differential equations --- particle accelerator --- coupling impedance --- dual integral equations --- Clenshaw-Curtis quadrature --- steepest descent method --- logarithmic singularities --- Cauchy singularity --- highly oscillatory integrals --- second-order --- nonoscillatory solutions --- oscillatory solutions --- delay differential equations --- Fredholm integral equations --- multiresolution analysis --- unitary extension principle --- oblique extension principle --- B-splines --- wavelets --- tight framelets --- Swift–Hohenberg type of equation --- surfaces --- narrow band domain --- closest point method --- operator splitting method

Multiscale Turbulent Transport

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ISBN: 9783039282128 9783039282135 Year: Pages: 210 DOI: 10.3390/books978-3-03928-213-5 Language: English
Publisher: MDPI - Multidisciplinary Digital Publishing Institute
Subject: Technology (General) --- General and Civil Engineering
Added to DOAB on : 2020-04-07 23:07:08
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Turbulent transport is currently a prominent and ongoing investigation subject at the interface of methodologies from theory to numerical simulations and experiments, and it covers several spatiotemporal scales. Mathematical analysis, physical modelling, and engineering applications represent different facets of a classical, long-standing problem that is still far from being thoroughly comprehended. The goal of this Special Issue is to outline recent advances of such subjects as multiscale analysis in turbulent transport processes, Lagrangian and Eulerian descriptions of turbulence, advection of particles and fields in turbulent flows, ideal or nonideal turbulence (unstationary/inhomogeneous/anisotropic/compressible), turbulent flows in biofluid mechanics and magnetohydrodynamics, and the control and optimization of turbulent transport. The SI is open to regular articles, review papers focused on the state of the art and the progress made over the last few years, and new research trends.

Advanced Numerical Methods in Applied Sciences

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ISBN: 9783038976660 9783038976677 Year: Pages: 306 DOI: 10.3390/books978-3-03897-667-7 Language: English
Publisher: MDPI - Multidisciplinary Digital Publishing Institute
Subject: Science (General) --- Mathematics
Added to DOAB on : 2019-06-26 08:44:06
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The use of scientific computing tools is currently customary for solving problems at several complexity levels in Applied Sciences. The great need for reliable software in the scientific community conveys a continuous stimulus to develop new and better performing numerical methods that are able to grasp the particular features of the problem at hand. This has been the case for many different settings of numerical analysis, and this Special Issue aims at covering some important developments in various areas of application.

Keywords

time fractional differential equations --- mixed-index problems --- analytical solution --- asymptotic stability --- conservative problems --- Hamiltonian problems --- energy-conserving methods --- Poisson problems --- Hamiltonian Boundary Value Methods --- HBVMs --- line integral methods --- constrained Hamiltonian problems --- Hamiltonian PDEs --- highly oscillatory problems --- boundary element method --- finite difference method --- floating strike Asian options --- continuous geometric average --- barrier options --- isogeometric analysis --- adaptive methods --- hierarchical splines --- THB-splines --- local refinement --- linear systems --- preconditioners --- Cholesky factorization --- limited memory --- Volterra integral equations --- Volterra integro–differential equations --- collocation methods --- multistep methods --- convergence --- B-spline --- optimal basis --- fractional derivative --- Galerkin method --- collocation method --- spectral (eigenvalue) and singular value distributions --- generalized locally Toeplitz sequences --- discretization of systems of differential equations --- higher-order finite element methods --- discontinuous Galerkin methods --- finite difference methods --- isogeometric analysis --- B-splines --- curl–curl operator --- time harmonic Maxwell’s equations and magnetostatic problems --- low rank completion --- matrix ODEs --- gradient system --- ordinary differential equations --- Runge–Kutta --- tree --- stump --- order --- elementary differential --- edge-histogram --- edge-preserving smoothing --- histogram specification --- initial value problems --- one-step methods --- Hermite–Obreshkov methods --- symplecticity --- B-splines --- BS methods --- hyperbolic partial differential equations --- high order discontinuous Galerkin finite element schemes --- shock waves and discontinuities --- vectorization and parallelization --- high performance computing --- generalized Schur algorithm --- null-space --- displacement rank --- structured matrices --- stochastic differential equations --- stochastic multistep methods --- stochastic Volterra integral equations --- mean-square stability --- asymptotic stability --- numerical analysis --- numerical methods --- scientific computing --- initial value problems --- one-step methods --- Hermite–Obreshkov methods --- symplecticity --- B-splines --- BS methods

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MDPI - Multidisciplinary Digital Publishing Institute (3)


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english (3)


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2020 (2)

2019 (1)