On linear ODEs with a time singularity of the first kind and unsmooth inhomogeneity
type: Item
instance of: scholarly article
title: On linear ODEs with a time singularity of the first kind and unsmooth inhomogeneity
zbMATH Open document ID: 1316.34025
author: Jana Burkotová
author: Irena Rachůnková
author: Svatoslav Staněk
author: E. B. Weinmüller
published in: Boundary Value Problems
publication date: 2014-12-12T00:00:00Z
review text: The solvability of the boundary value problem \[ y'(t)=\frac{M}{t}y(t)+\frac{f(t)}{t},\;\;t\in(0,1], \] \[ B_0y(0)+B_1y(1)\beta \] is studied in this paper. Here \(M\in \mathbb R^{n\times n},\;B_0,B_1\in \mathbb R^{m\times n}, m\leq n, \beta\in \mathbb R^m,\) and \(f\in C[0,1]\) but \(f(t)/t\) may not be integrable on \([0,1].\) A result guaranteeing existence and uniqueness of a \(C[0,1]\)-solution is obtained as a sequence of results which infer that the considered differential equation has a unique solution satisfying the initial condition \(B_0y(0)=\beta\) or the terminal condition \(B_1y(1)=\beta.\) The results for the initial value problem are obtained under the assumption that all eigenvalues of \(M\) are zero or have negative real parts, while those for the terminal value problem are obtained under the assumtion that all eigenvalues of \(M\) are zero or have positive real parts. Collocation schemes are proposed also for the numerical treatment of the considered problems.
reviewed by: Petio S. Kelevedjiev
Mathematics Subject Classification ID: 34B16
Mathematics Subject Classification ID: 34A12
Mathematics Subject Classification ID: 34A30
Mathematics Subject Classification ID: 34B05
Mathematics Subject Classification ID: 65L10
zbMATH DE Number: 6380157
zbMATH Keywords: linear systems of ODEs
zbMATH Keywords: singular boundary value problem
zbMATH Keywords: time singularity of the first kind
zbMATH Keywords: nonsmooth inhomogeneity
zbMATH Keywords: existence and uniqueness
zbMATH Keywords: collocation method
zbMATH Keywords: convergence
Wikidata QID: Q59320625
describes a project that uses: bvpsuite
describes a project that uses: avalanche.f
MaRDI profile type: Publication
full work available at URL: s13661-014-0183-6
OpenAlex ID: W2128230390
cites work: Dead core problems for singular equations with \(\varphi \)-Laplacian
cites work: Continuous dependence in front propagation of convective reaction-diffusion equations
cites work: Analysis and numerical simulation of positive and dead-core solutions of singular two-point boundary value problems
cites work: Analysis and numerical solutions of positive and dead core solutions of singular Sturm-Liouville problems
cites work: Difference Methods for Boundary Value Problems with a Singularity of the First Kind
cites work: Collocation for Singular Boundary Value Problems of Second Order
cites work: Analytical and numerical treatment of a singular initial value problem in avalanche modeling.
cites work: On boundary value problems for systems of linear generalized ordinary differential equations with singularities
cites work: Q4658838
cites work: Q5293000
cites work: The integral representation of solutions to a boundary value problem on the half-line for a system of linear ODEs with singularity of first kind
cites work: On certain boundary value problems for second-order linear ordinary differential equations with singularities
cites work: Slowly growing solutions of singular linear functional differential systems
cites work: Two-point boundary value problems for higher-order linear differential equations with strong singularities
cites work: On boundary value problems for linear differential systems with singularities
cites work: Estimates for the Cauchy function of linear singular differential equations and some applications
cites work: A smooth solution to a linear system of singular ODEs
cites work: Collocation Methods for Singular Boundary Value Problems
cites work: On the Boundary Value Problem for Systems of Ordinary Differential Equations with a Singularity of the Second Kind
cites work: The Application of Runge-Kutta Schemes to Singular Initial Value Problems
cites work: A collocation code for singular boundary value problems in ordinary differential equations
cites work: Q2960806
cites work: Q5848416
cites work: Initial value problems for systems of ordinary first and second order differential equations with a singularity of the first kind
cites work: Asymptotically correct error estimation for collocation methods applied to singular boundary value problems
cites work: Q3561647
DOI: 10.1186/S13661-014-0183-6
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description: scientific article; zbMATH DE number 6380157