In this paper, we introduce a method for computing rigorous local inclusions of solutions of Cauchy problems for nonlinear heat equations for complex time values. The proof is constructive and provides explicit bounds for the inclusion o...
Sovanna Mean   Koichi Unami   Hisashi Okamoto   Masayuki Fujihara   
Applied Mathematics and Computation 415 126730-126730 2022年2月 [査読有り]
Determining water surface profiles of steady open channel flows in a one-dimensional bounded domain is one of the well-trodden topics in conventional hydraulic engineering. However, it involves Dirichlet problems of scalar first-order quasilinear ...
Japan Journal of Industrial and Applied Mathematics 38(1) 79-103 2021年2月 [査読有り]
Abstract
Stationary waves of constant shape and constant propagation speed on rotational flows of two layers are computed numerically. Two layers are assumed to be of distinct constant vorticity distributions. Three different kinds of waves of fi...
We consider two-dimensional progressive water-waves, which propagate with a constant speed and a constant shape. Fluid motion is assumed to be irrotational. Trajectories in a coordinate system attached to the wave are easily computed by drawing co...