Bulletin of the Korean Mathematical Society 50(3) 963-982 2013年5月 [査読有り]
The Galerkin method has been developed mainly for 2nd order differential equations. To get numerical solutions, there are some choices of Riesz bases for the approximation subspace V-j subset of L-2. In this paper we shall propose a uniform approa...
On the Stokes and Navier-Stokes equations in a perturbed half-space
Takayuki, Kubo; Yoshihiro, Shibata
Advances in Differentical Equations 10(6) 695-720 2005年1月 [査読有り]
Numerical existence theorem for solutions of two-point boundary value problems of nonlinear differential equations
Nonlinear Theory and Its Applications, IEICE 1(1) 105-118 2010年1月
In this paper, a numerical method is presented for verifying the existence and uniqueness of solutions to two-point boundary value problems of nonlinear ordinary differential equations. Taking into account every error of numerical computations suc...