Stiff systems of ordinary differential equations. Part 1. Completely stiff, homogeneous systems

J. J. Mahony, J. J. Shepherd
1981 The Journal of the Australian Mathematical Society Series B Applied Mathematics  
For the completely stiff real homogeneous system ex = A(t, e)x, where e is a small positive parameter, a method is given for the construction of a basis for the solution space. If A has n linearly independent eigenvector functions, then there exists a choice of these, {s,}, with corresponding eigenvalue functions {\}, such that there is a local basis for solution, that takes the form v,.]exp[ £ -'/\]}, where v, is a vector that tends to zero with e. In general, a basis of this form exists only
more » ... s form exists only on an interval in which the distinct eigenvalues have their real parts ordered. A construction is provided for continuing any solution across the boundaries of any such interval. These results are proved for a finite or infinite interval for which there are only a finite number of points at which the ordering of the real parts of eigenvalues changes.
doi:10.1017/s0334270000000047 fatcat:4nobx4am6bdthfhwse3a5oemcu