Ph.D Thesis | |

Ph.D Student | Pidgirnyak Anna |
---|---|

Subject | Stability of Finite Difference Approximations for Parabolic Systems with Constant Coefficients |

Department | Department of Applied Mathematics |

Supervisor | PROFESSOR EMERITUS Moshe Goldberg |

This thesis deals with *L*_{2}-stability
of a well-known family of finite difference approximations to multi-space, well-posed
parabolic initial-value problems of the form

where
is an unknown *m*-vector, and
*A _{pq}*,

The first part of this work provides a survey of the mathematical tools and the
literature pertaining to the subject matter. The heart of this survey consists
of a detailed discussion regarding the theory of Goldberg (1998) and of Sun and
Yuan (2000), which offer sufficient stability conditions for our schemes in the
classical case where the leading matrix coefficients *A _{pq}* of
the initial-value problem are Hermitian.

The second part of the thesis presents new results, which deal with the triangular
case, in which the matrices *A _{pq}* are upper triangular with
real eigenvalues. We provide sufficient stability conditions for the

We conclude by a brief discussion regarding the general case, where our initial-value problem cannot be reduced to either Hermitian or triangular form.