scholarly journals KANTBP 4M Program for Solving the Scattering Problem for a System of Ordinary Second-Order Differential Equations

2020 ◽  
Vol 226 ◽  
pp. 02008
Author(s):  
Galmandakh Chuluunbaatar ◽  
Alexander A. Gusev ◽  
Ochbadrakh Chuluunbaatar ◽  
Sergue I. Vinitsky ◽  
Luong Le Hai
Keyword(s):  
Differential Equations ◽  
Hermite Interpolation ◽  
Scattering Problem ◽  
Second Order ◽  
The Finite Element Method ◽  
Multichannel Scattering ◽  
Reaction Region ◽  
Interpolation Polynomials ◽  
Complex Valued ◽  
Hermite Interpolation Polynomials

We report an upgrade of the program KANTBP 4M implemented in the computer algebra system MAPLE for solving, with a given accuracy, the multichannel scattering problem, which is reduced to a boundary-value problem for a system of ordinary differential equations of the second order with continuous or piecewise continuous real or complex-valued coeffcients. The solution over a finite interval is subject to mixed homogeneous boundary conditions: Dirichlet and/or Neumann, and/or of the third kind. The discretization of the boundary problem is implemented by means of the finite element method with the Lagrange or Hermite interpolation polynomials. The effciency of the proposed algorithm is demonstrated by solving a multichannel scattering problem with coupling of channels in both the reaction region and the asymptotic one.

scholarly journals On a Class of Hermite Interpolation Polynomials for Nonlinear Second Order Partial Differential Operators

2018 ◽  
Vol 173 ◽  
pp. 03023
Author(s):  
Leonid A. Yanovich ◽  
Marina V. Ignatenko
Keyword(s):  
Hermite Interpolation ◽  
Differential Operators ◽  
Second Order ◽  
Chebyshev System ◽  
Partial Differential ◽  
Differentiable Functions ◽  
Partial Differential Operators ◽  
Operator Interpolation ◽  
Interpolation Polynomials ◽  
Hermite Interpolation Polynomials

This article is devoted to the problem of construction of Hermite interpolation formulas with knots of the second multiplicity for second order partial differential operators given in the space of continuously differentiable functions of two variables. The obtained formulas contain the Gateaux differentials of a given operator. The construction of operator interpolation formulas is based on interpolation polynomials for scalar functions with respect to an arbitrary Chebyshev system of functions. An explicit representation of the interpolation error has been obtained.

scholarly journals Polynomial interpolation on the unit sphere and some properties of its integral means

Filomat ◽  
2019 ◽  
Vol 33 (15) ◽  
pp. 4697-4715
Author(s):  
Manha van ◽  
Khiema van
Keyword(s):  
Unit Sphere ◽  
Hermite Interpolation ◽  
Polynomial Interpolation ◽  
Convergence Properties ◽  
Integral Means ◽  
Interpolation Polynomials ◽  
Hermite Interpolation Polynomials

We study Hermite interpolation on the unit sphere. We give poised Hermite schemes on parallel circles with odd and even number of points on each circle. We also prove continuity and convergence properties of integral means of Hermite interpolation polynomials.

scholarly journals Interpolation Hermite Polynomials For Finite Element Method

2018 ◽  
Vol 173 ◽  
pp. 03009 ◽  
Author(s):  
Alexander Gusev ◽  
Sergue Vinitsky ◽  
Ochbadrakh Chuluunbaatar ◽  
Galmandakh Chuluunbaatar ◽  
Vladimir Gerdt ◽  
...  
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Hermite Interpolation ◽  
Hermite Polynomials ◽  
High Accuracy ◽  
High Order ◽  
Analytic Calculation ◽  
Interpolation Polynomials ◽  
Finite Element Schemes ◽  
Hermite Interpolation Polynomials

We describe a new algorithm for analytic calculation of high-order Hermite interpolation polynomials of the simplex and give their classification. A typical example of triangle element, to be built in high accuracy finite element schemes, is given.

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