Contributions to Books:
S. Stanek, G. Pulverer, E. Weinmüller:
"Analysis and numerical simulation of positive and dead core solutions of singular two-point boundary value problems";
in: "ASC Report 18/2007",
issued by: Institute for Analysis and Scientific Computing;
Vienna University of Technology,
Wien,
2007,
ISBN: 978-3-902627-00-1.
English abstract:
We investigate the solvability of the Dirichlet boundary value problem
u′′(t) = g(u(t)), ≥ 0, u(0) = 1, u(1) = 1,
where is a nonnegative parameter. We discuss the existence of multiple positive
solutions and show that for certain values of , there also exist solutions that
vanish on a subinterval [ , 1 − ] ⊂ (0, 1), the so-called dead core solutions. In
order to illustrate the theoretical findings, we present computational results for
g(u) = 1/√u, computed using the collocation method implemented in bvpsuite,
a new version of the standard MATLAB code sbvp1.0.
Keywords:
Singular Dirichlet boundary value problem, positive solution, dead
Electronic version of the publication:
http://www.asc.tuwien.ac.at/preprint/2007/asc18x2007.pdf
Created from the Publication Database of the Vienna University of Technology.