Numerical Analysis or Numerical Method in Symmetry

• Main Author: Cesarano, Clemente (auth)
• Format: Electronic Book Chapter
• Language: English
• Published: MDPI - Multidisciplinary Digital Publishing Institute 2020
• Subjects: risk assessment; complex Lagrangian; effective order; logarithmic singularities; Swift-Hohenberg type of equation; Cauchy singularity; differential equations; unitary extension principle; oscillatory solutions; coupling impedance; Fredholm integral equations; dual integral equations; composition properties; delay differential equations; chemical reaction; Noether symmetries; symplectic Runge-Kutta methods; order conditions; non-homogeneous; wavelets; multiresolution analysis; narrow band domain; pseudo-Chebyshev polynomials; highly oscillatory integrals; tight framelets; Chebyshev polynomials; nonoscillatory solutions; ignition hazard; quad-colored trees; general solution; operator splitting method; fourth-order ODEs; offshore plant; special function; second-order; surfaces; numerical analysis; effective field strength; closest point method; oblique extension principle; heat generation; B-splines; Runge-Kutta type methods; orthogonality properties; Frobenius method; hamiltonian systems; B-series; k-hypergeometric series; particle accelerator; first integrals; partitioned runge-kutta methods; Clenshaw-Curtis quadrature; recurrence relations; thin needle; nanofluid; Hamiltonian system; k-hypergeometric differential equations; steepest descent method; symplecticity; fourth-order
• Online Access: DOAB: download the publication; DOAB: description of the publication

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.