3月19日(金) 11:00 -- 12:30 西田 詩 (鹿児島大学理学部)
``Kowalevsky Theorem and Finite Difference Scheme''
＜研究発表要旨＞
We consider a partial differential equation
\frac{\partial u}{\partial t}
= \sum_{j=1}^{J} A_{j}(t, x, u) \frac{\partial u}{\partial x_{j}}
+ B(t, x, u) in t > 0, |x| < \rho ,
where x is a J-dimensional complex vector and u is a N-dimensional complex
valued function, with the initial value
u(0, x) = \varphi(x), |x|<\rho_{0}.
We assume some smoothness and analyticity of coefficients and initial value,
and we apply finite difference method to this problem. We show ,under certain
assumption, the approximate solution uniformly converges to the exact one
in some compact domain.