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추상목,김영희 한국전산응용수학회 2005 Journal of applied mathematics & informatics Vol.19 No.1-2
A finite element scheme is considered for the viscous Cahn-Hilliard equation with the nonconstant gradient energy coefficient. The scheme inherits energy decay property and mass conservation as for the classical solution. We obtain the corresponding error estimate using the extended Lax-Richtmyer equivalence theorem.
추상목 한국전산응용수학회 2007 Journal of applied mathematics & informatics Vol.23 No.1
Finite difference schemes are considered for a generalization of the Cahn-Hilliard equation with Neumann boundary conditions and the Kuramoto- Sivashinsky equation with a periodic boundary condition, which is of the type ut+ @2 @x2 g(u, ux, uxx) = f(u, ux, uxx). Stability and L1 error estimates of approximate solutions for the corresponding schemes are obtained using the extended Lax-Richtmyer equivalence theorem.
Optimization of parameters in biological systems of delay differential equations
추상목 한국전산응용수학회 2008 Journal of applied mathematics & informatics Vol.26 No.3-4
Biological systems with both protein-protein and protein-gene interactions can be modeled by differential equations for concentrations of the proteins with time-delay terms because of the time needed for DNA transcription to mRNA and translation of mRNA to protein. Values of some parameters in the mathematical model can not be measured owing to the difficulty of xperiments. Also values of some parameters obtained in a normal stress condition can be changed under pathological stress stimuli. Thus it is important to find the effective way of determining parameters values. One approach is to use optimization algorithms. Here we construct an optimal system used to find optimal parameters in the equations with nonnegative time delays and apply this optimization result to the Nuclear factor-kB pathway.
Finite difference schemes for a generalized Calcium diffusion equation
추상목,이남용 영남수학회 2008 East Asian mathematical journal Vol.24 No.4
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^{∞} error estimates of approximate solutions for the corresponding schemes are obtained using the extended Lax-Richtmyer equivalence theorem.
Finite difference schemes for Calcium diffusion equations
추상목 한국전산응용수학회 2008 Journal of applied mathematics & informatics Vol.26 No.1
Finite difference schemes are considered for a Ca²+ diffusion equations, which discribe Ca²+ buffering by using stationary and mobile buffers. Stability and L1 error estimates of approximate solutions for the corresponding schemes are obtained using the extended Lax-Richtmyer equivalence theorem.
REMARKS ON CRITERIA FOR THE EXISTENCE OF A POSITIVE EQUILIBRIUM IN REACTION NETWORKSy
추상목 한국전산응용수학회 2011 Journal of applied mathematics & informatics Vol.29 No.3
It is interesting to know the behavior of a network from its structure. One interesting topic is to find a relation between the existence of a positive equilibrium of the reaction network and its structure. One approach to study this topic is using the concept of deficiency. Another is using some conditions on nodes, which can apply to large-size networks compared to deficiency. In this work, we show the relation between deficiency and the conditions.
A GRAPHICAL ALGORITHM FOR CALCULATING THE RANKS OF COMPLEX REACTION NETWORKS
추상목,이남용 한국전산응용수학회 2012 Journal of applied mathematics & informatics Vol.30 No.5
We present a graphical algorithm and theorems for calculating the ranks of reaction networks. The ranks are needed to study behaviors of the networks from their structures. This approach can graphically simplify complex networks for the calculation. We show an example of a large network for the practical advantage.
A conservative nonlinear difference scheme for the viscous Cahn-Hilliard equation
추상목,정상권 한국전산응용수학회 2004 Journal of applied mathematics & informatics Vol.16 No.-
Numerical solutions for the viscous Cahn-Hilliard equation are con-sidered using the Crank-Nicolson type nite dierence method which conservesthe mass. The corresponding stability and error analysis of the scheme are shown.The decay speeds of the solution in H1-norm are shown. We also compare theevolution of the viscous Cahn-Hilliard equation with that of the Cahn-Hilliardequation numerically and computationally, which has been given as an open ques-tion in Novick-Cohen[13].
Stochastic differential equation models for extracellular signal-regulated kinase pathways
추상목,김영희 한국전산응용수학회 2013 Journal of applied mathematics & informatics Vol.31 No.3
There exist many deterministic models for signaling pathways in systems biology. However the models do not consider the stochastic properties of the pathways, which means the models fit well with experimental data in certain situations but poorly in others. Incorporating stochasticity into deterministic models is one way to handle this problem. In this paper the way is used to produce stochastic models based on the deterministic differential equations for the published extracellular signal-regulated kinase (ERK) pathway. We consider strong convergence and stability of the numerical approximations for the stochastic models.