On nonlinear singular BVPs with nonsmooth data. Part 2: Convergence of collocation methods

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61989592%3A15310%2F22%3A73610022" target="_blank" >RIV/61989592:15310/22:73610022 - isvavai.cz</a>
Result on the web
<a href="https://www.sciencedirect.com/science/article/pii/S0168927421002440" target="_blank" >https://www.sciencedirect.com/science/article/pii/S0168927421002440</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1016/j.apnum.2021.08.016" target="_blank" >10.1016/j.apnum.2021.08.016</a>

Result language
angličtina
Original language name
On nonlinear singular BVPs with nonsmooth data. Part 2: Convergence of collocation methods
Original language description
We discuss numerical solution of boundary value problems for systems of nonlinear ordinary differential equations with a time singularity, x'(t) = M(t) t f (t,x(t)) x(t) + t , t is an element of (0, 1], b(x(0), x(1)) = 0, where M : [0, 1] -Rnxn and f : [0, 1] x Rn -Rn are continuous matrix-valued and vector-valued functions, respectively. Moreover, b: Rn x Rn -Rn is a continuous nonlinear mapping which is specified according to a spectrum of the matrix M(0) to guarantee the BVP to be well-posed. For the case where M(0) has eigenvalues with nonzero real parts, we prove new convergence results for the collocation method and analytical results about the necessary smoothness of the solution to the problem required in the numerical analysis. We illustrate the theory by means of numerical examples.
Czech name
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Czech description
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Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
—
OECD FORD branch
10101 - Pure mathematics

Project
<a href="/en/project/GA14-06958S" target="_blank" >GA14-06958S: Singularities and impulses in boundary value problems for nonlinear ordinary differential equations</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year
2022
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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