Temat: singular boundary value problems

Skocz do pozycji: 1.

Tytuł:: Collocation methods for the solution of eigenvalue problems for singular ordinary differential equations
Autorzy:: Auzinger, W.
Karner, E.
Koch, O.
Weinmuller, E.
Tematy:: polynomial collocation
singular boundary value problems
linear and nonlinear eigenvalue problems; Pokaż więcej
Wydawca:: Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
Powiązania:: https://bibliotekanauki.pl/articles/255635.pdf Link otwiera się w nowym oknie
Opis:: We demonstrate that eigenvalue problems for ordinary differential equations can be recast in a formulation suitable for the solution by polynomial collocation. It is shown that the well-posedness of the two formulations is equivalent in the regular as well as in the singular case. Thus, a collocation code equipped with asymptotically correct error estimation and adaptive mesh selection can be successfully applied to compute the eigenvalues and eigenfunctions efficiently and with reliable control of the accuracy. Numerical examples illustrate this claim.
Dostawca treści:: Biblioteka Nauki

Artykuł

Skocz do pozycji: 2.

Tytuł:: Solving boundary value problems in the open source software R: package bvpSolve
Autorzy:: Mazzia, F.
Cash, J. R.
Soetaert, K.
Tematy:: ordinary differential equations
boundary value problems
singular perturbation problems
test problems
Fortran
R; Pokaż więcej
Wydawca:: Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
Powiązania:: https://bibliotekanauki.pl/articles/255850.pdf Link otwiera się w nowym oknie
Opis:: The R package bvpSolve for the numerical solution of Boundary Value Problems (BVPs) is presented. This package is free software which is distributed under the GNU General Public License, as part of the R open source software project. It includes some well known codes to solve boundary value problems of ordinary differential equations (ODEs) and differential algebraic equations (DAEs). In addition to the packages already available for solving initial value problems, the new package now allows non expert users to efficiently solve boundary value problems in the problem solving environment R.
Dostawca treści:: Biblioteka Nauki

Artykuł

Skocz do pozycji: 3.

Tytuł:: On solutions of integral equations with analytic kernels and rotations
Autorzy:: Nguyen, Mau
Nguyen, Tuan
Tematy:: integral operators
singular integral equations
algebraic operators
Riemann boundary value problems; Pokaż więcej
Wydawca:: Polska Akademia Nauk. Instytut Matematyczny PAN
Powiązania:: https://bibliotekanauki.pl/articles/1311183.pdf Link otwiera się w nowym oknie
Opis:: We deal with a class of integral equations on the unit circle in the complex plane with a regular part and with rotations of the form (*) x(t) + a(t)(Tx)(t) = b(t), where $T = M_{n₁,k₁} ... M_{n_m,k_m}$ and $M_{n_j,k_j}$ are of the form (3) below. We prove that under some assumptions on analytic continuation of the given functions, (*) is a singular integral equation for m odd and is a Fredholm equation for m even. Further, we prove that T is an algebraic operator with characteristic polynomial $P_T(t) = t³ - t$. By means of the Riemann boundary value problems, we give an algebraic method to obtain all solutions of equation (*) in closed form.
Dostawca treści:: Biblioteka Nauki

Artykuł

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