• Journal of applied mathematics & informatics
• /
• v.26 no.1_2
• /
• pp.299-306
• /
• 2008

Finite difference schemes are considered for a $Ca^{2+}$ diffusion equations, which discribe $Ca^{2+}$ buffering by using stationary and mobile buffers. Stability and $L^\infty$ error estimates of approximate solutions for the corresponding schemes are obtained using the extended Lax-Richtmyer equivalence theorem.

• Journal of the Korean Society for Industrial and Applied Mathematics
• /
• v.3 no.1
• /
• pp.55-69
• /
• 1999

In this paper we analyze the error estimates for a single-phase nonlinear Stefan problem with Neumann boundary conditions. We apply the modified Crank-Nicolson method to get the optimal order of error estimates in the temporal direction.

• Bulletin of the Korean Mathematical Society
• /
• v.52 no.5
• /
• pp.1445-1465
• /
• 2015

In this paper, the long time behavior of the convective Cahn-Hilliard equation in two dimensions is considered, semidiscrete and completely discrete spectral approximations are constructed, error estimates of optimal order that hold uniformly on the unbounded time interval $0{\leq}t<{\infty}$ are obtained.

• East Asian mathematical journal
• /
• v.24 no.4
• /
• pp.407-414
• /
• 2008

Finite difference schemes are considered for a $Ca^{2+}$ diffusion equations with damping and convection terms, which describe $Ca^{2+}$ buffering by using stationary and mobile buffers. Stability and $L^{\infty}$ error estimates of approximate solutions for the corresponding schemes are obtained using the extended Lax-Richtmyer equivalence theorem.

• Journal of applied mathematics & informatics
• /
• v.6 no.1
• /
• pp.15-30
• /
• 1999

In this paper the second order semi-discrete and full dis-crete generalized difference schemes for one dimensional parabolic equa-tions are constructed and the optimal order $H^1$ , $L^2$ error estimates and superconvergence results in TEX>$H^1$ are obtained. The results in this paper perfect the theory of generalized difference methods.

• Journal of applied mathematics & informatics
• /
• v.27 no.5_6
• /
• pp.1247-1256
• /
• 2009

Finite difference schemes are considered for a nonlinear $Ca^{2+}$ diffusion equations with stationary and mobile buffers. The scheme inherits mass conservation as for the classical solution. Stability and $L^{\infty}$ error estimates of approximate solutions for the corresponding schemes are obtained. using the extended Lax-Richtmyer equivalence theorem.

• East Asian mathematical journal
• /
• v.26 no.5
• /
• pp.615-626
• /
• 2010

In this paper, we analyze discontinuous Galerkin methods with penalty terms, namly symmetric interior penalty Galerkin methods, to solve nonlinear parabolic equations. We construct finite element spaces on which we develop fully discrete approximations using extrapolated Crank-Nicolson method. We adopt an appropriate elliptic-type projection, which leads to optimal ${\ell}^{\infty}$ ($L^2$) error estimates of discontinuous Galerkin approximations in both spatial direction and temporal direction.

• Journal of the Korean Data and Information Science Society
• /
• v.19 no.4
• /
• pp.1219-1231
• /
• 2008

The main object of this paper is to develop a leave-one-out(LOO) bound of all pairwise comparison error correcting output codes (APC-ECOC). To avoid using classifiers whose corresponding target values are 0 in APC-ECOC and requiring pilot estimates we developed a bound based on mean misclassification probability(MMP). It can be used to tune kernel hyperparameters. Our empirical experiment using kernel mean squared estimate(KMSE) as the binary classifier indicates that the bound leads to good estimates of kernel hyperparameters.

• Journal of applied mathematics & informatics
• /
• v.11 no.1_2
• /
• pp.185-199
• /
• 2003

In this paper, we apply finite element Galerkin method to a single-phase quasi-linear Stefan problem with a forcing term. We consider the existence and uniqueness of a semidiscrete approximation and optimal error estimates in $L_2$, $L_{\infty}$, $H_1$ and $H_2$ norms for semidiscrete Galerkin approximations we derived.

• Journal of applied mathematics & informatics
• /
• v.23 no.1_2
• /
• pp.43-55
• /
• 2007

In this paper, an $H^1-Galerkin$ mixed finite element method is used to approximate the solution as well as the flux of Burgers' equation. Error estimates have been derived. The results of the numerical experiment show the efficacy of the mixed method and justifies the theoretical results obtained in the paper.