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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.
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 rungekutta methods  symplecticity  hamiltonian systems  RungeKutta type methods  fourthorder ODEs  order conditions  Bseries  quadcolored trees  khypergeometric differential equations  nonhomogeneous  khypergeometric series  special function  general solution  Frobenius method  Chebyshev polynomials  pseudoChebyshev polynomials  recurrence relations  differential equations  composition properties  orthogonality properties  numerical analysis  heat generation  chemical reaction  thin needle  nanofluid  fourthorder  nonoscillatory solutions  oscillatory solutions  delay differential equations  particle accelerator  coupling impedance  dual integral equations  ClenshawCurtis quadrature  steepest descent method  logarithmic singularities  Cauchy singularity  highly oscillatory integrals  secondorder  nonoscillatory solutions  oscillatory solutions  delay differential equations  Fredholm integral equations  multiresolution analysis  unitary extension principle  oblique extension principle  Bsplines  wavelets  tight framelets  Swift–Hohenberg type of equation  surfaces  narrow band domain  closest point method  operator splitting method
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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 nonNewtonian 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.
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  Kellerbox 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 gJitter flow  inclined stretching sheet  heat source/sink  Magnetohydrodynamic (MHD)  Jefferey, Maxwell and OldroydB fluids  Cattaneo–Christov heat flux  homogeneous–heterogeneous reactions  analytical technique  Numerical technique  viscous fluid  Caputo–Fabrizio timefractional 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  homogeneousheterogeneous reactions  integer and noninteger order derivatives  GOW/GOEG nanofluids  Marangoni convection  FDE12 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 nonNewtonian 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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