Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
8902591 | Applied Numerical Mathematics | 2018 | 28 Pages |
Abstract
We study boundary value problems for systems of nonlinear ordinary differential equations with a time singularity,xâ²(t)=M(t)tx(t)+f(t,x(t))t,tâ(0,1],b(x(0),x(1))=0, where M:[0,1]âRnÃn and f:[0,1]ÃRnâRn are continuous matrix-valued and vector-valued functions, respectively. Moreover, b:RnÃRnâRn is a continuous nonlinear mapping which is specified according to a spectrum of the matrix M(0). For the case that M(0) has eigenvalues with nonzero real parts, we prove new results about existence of at least one continuous solution on the closed interval [0,1] including the singular point, t=0. We also formulate sufficient conditions for uniqueness. The theory is illustrated by a numerical simulation based on the collocation method.
Related Topics
Physical Sciences and Engineering
Mathematics
Computational Mathematics
Authors
Jana Burkotová, Irena Rachůnková, Svatoslav StanÄk, Ewa B. Weinmüller, Stefan Wurm,