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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

Symmetry and Fluid Mechanics

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ISBN: 9783039284269 9783039284276 Year: Pages: 446 DOI: 10.3390/books978-3-03928-427-6 Language: English
Publisher: MDPI - Multidisciplinary Digital Publishing Institute
Subject: Technology (General) --- General and Civil Engineering
Added to DOAB on : 2020-04-07 23:07:09
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Since the 1980s, attention has increased in the research of fluid mechanics due to its wide application in industry and phycology. Major advances have occurred in the modeling of key topics such Newtonian and non-Newtonian fluids, nanoparticles, thermal management, and physiological fluid phenomena in biological systems, which have been published in this Special Issue on symmetry and fluid mechanics for Symmetry. Although, this book is not a formal textbook, it will be useful for university teachers, research students, and industrial researchers and for overcoming the difficulties that occur when considering the nonlinear governing equations. For such types of equations, obtaining an analytic or even a numerical solution is often more difficult. This book addresses this challenging job by outlining the latest techniques. In addition, the findings of the simulation are logically realistic and meet the standard of sufficient scientific value.

Keywords

stagnation point flow --- numerical solution --- magnetic field --- nanofuid --- unsteady rotating flow --- porous medium --- aqueous suspensions of CNT’s --- nonlinear thermal radiation --- viscous dissipation effect --- HAM --- chemical reaction --- activation energy --- peristalsis --- couple stress fluid --- nanoparticle --- Keller-box method --- Newtonian heating --- nonlinear thermal radiation --- nonlinear stretching cylinder --- homogeneous/heterogeneous reactions --- nanofluid --- steady laminar flow --- nanofluid --- heat source/sink --- magnetic field --- stretching sheet --- SWCNT/MWCNT nanofluid --- thin needle --- classical and fractional order problems --- APCM technique --- SWCNTs --- MWCNTs --- stretched surface --- rotating system --- nanofluid --- MHD --- thermal radiation --- HAM --- nonlinear hydroelastic waves --- uniform current --- thin elastic plate --- solitary waves --- PLK method --- Permeable walls --- suction/injection --- nanofluids --- porous medium --- mixed convection --- magnetohydrodynamic (MHD) --- dual solution --- stability analysis --- Darcy Forchheimer model --- nanofluid --- exponential sheet --- Jeffrey fluid --- laminar g-Jitter flow --- inclined stretching sheet --- heat source/sink --- Magnetohydrodynamic (MHD) --- Jefferey, Maxwell and Oldroyd-B fluids --- Cattaneo–Christov heat flux --- homogeneous–heterogeneous reactions --- analytical technique --- Numerical technique --- viscous fluid --- Caputo–Fabrizio time-fractional derivative --- Laplace and Fourier transformations --- side walls --- oscillating shear stress --- forced convection --- microducts --- Knudsen number --- Nusselt number --- artificial neural networks --- particle swarm optimization --- Casson fluid --- chemical reaction --- cylinder --- heat generation --- magnetohydrodynamic (MHD) --- slip --- Carreau fluid --- Cattaneo–Christov heat flux model --- convective heat boundary condition --- temperature dependent thermal conductivity --- homogeneous-heterogeneous reactions --- integer and non-integer order derivatives --- GO-W/GO-EG nanofluids --- Marangoni convection --- FDE-12 numerical method --- couple stress fluid --- Hafnium particles --- Couette–Poiseuille flow --- shooting method --- magnetic field --- Darcy–Brinkman porous medium --- viscous dissipation --- slip conditions --- porous dissipation --- permeable sheet --- stretchable rotating disk --- CNTs (MWCNTs and SWCNTs) --- velocity slip --- convective boundary condition --- OHAM --- Casson fluid model --- rotating rigid disk --- nanoparticles --- Magnetohydrodynamics (MHD) --- Oil/MWCNT nanofluid --- heat transfer --- finite volume method --- laminar flow --- slip coefficient --- microchannel --- arched surface --- nonlinear thermal radiation --- molecular diameter --- Al2O3 nanoparticles --- streamlines --- isotherms --- RK scheme --- peristaltic transport --- tapered channel --- porous medium --- smart pumping for hemodialysis --- thermal radiation --- compressible viscous flow --- symmetric linear equations --- generalized finite difference scheme --- kernel gradient free --- Lagrangian approach --- Newtonian and non-Newtonian fluids --- nanofluids and particle shape effects --- convective heat and mass transfer --- steady and unsteady flow problems --- multiphase flow simulations --- fractional order differential equations --- thermodynamics --- physiological fluid phenomena in biological systems

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MDPI - Multidisciplinary Digital Publishing Institute (2)


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CC by-nc-nd (2)


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english (2)


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2020 (2)