• East Asian mathematical journal
• /
• v.36 no.1
• /
• pp.81-90
• /
• 2020

Many compartment models assume a kinetically homogeneous amount of materials that have well-stirred compartments. However, based on observations from such processes, they have been heuristically fitted by exponential or gamma distributions even though biological media are inhomogeneous in real environments. Fractional differential equations using a specific kernel in Pharmacokinetic/Pharmacodynamic (PKPD) model are recently introduced to account for abnormal drug disposition. We discuss a tumor growth inhibition (TGI) model using fractional-order derivative from it. This represents a tumor growth delay by cytotoxic agents and additionally show variations in the equilibrium points by the change of fractional order. The result indicates that the equilibrium depends on the tumor size as well as a change of the fractional order. We find that the smaller the fractional order, the smaller the equilibrium value. However, a difference of them is the number of concavities and this indicates that TGI over time profile for fitting or prediction should be determined properly either fractional order or tumor sizes according to the number of concavities shown in experimental data.

• Journal of applied mathematics & informatics
• /
• v.8 no.3
• /
• pp.743-753
• /
• 2001

We provide local convergence results in affine form for inexact Newton-like as well as quasi-Newton iterative methods in a Banach space setting. We use hypotheses on the second or on the first and mth Frechet-derivative (m≥2 an integer) of the operator involved. Our results allow a wider choice of starting points since our radius of convergence can be larger than the corresponding one given in earlier results using hypotheses on the first-Frechet-derivative only. A numerical example is provided to illustrate this fact. Our results apply when the method is, for example, a difference Newton-like or update-Newton method. Furthermore, our results have direct applications to the solution of autonomous differential equations.

• Journal of the Korean Chemical Society
• /
• v.14 no.1
• /
• pp.127-131
• /
• 1970

The variational approach for the direct evaluation of the energy difference ${\Delta}$E is studied. The method is based on the differential equation corresponding to the integral Hellmann-Feynman formula. The ${\Delta}$E is given by the expectation value of the Hermitian operator which does not involve the 1/$r_{ij}$ term. Because of its variational nature of the method, the coupling problem of the differential equations which are encountered in perturbation treatment does not occur. The method is applied to the evaluation of the electric polarizabilities of the Helium isoelectronic series atoms. The result is in good agreement with the experiment. The method is compared with the recent works of Karplus et al.

• Geomechanics and Engineering
• /
• v.29 no.6
• /
• pp.667-681
• /
• 2022

This paper presents a thermoelastic analysis of variable thickness plates made of functionally graded materials (FGM) subjected to mechanical and thermal loads. The thermal load is applied to the plate as a temperature difference between the top and bottom surfaces. Temperature distribution in the plate is obtained using the steady-state heat equation. Except for Poisson's ratio, all mechanical properties of the plate are assumed to vary linearly along the thickness direction based on the volume fractions of ceramic and metal. The plate is resting on an elastic foundation modeled based on the Winkler foundation model. The governing equations are derived based on the third-order shear deformation theory (TSDT) and are solved numerically for various boundary conditions using the differential quadrature method (DQM). The effects of various parameters on the stress distribution and deflection of the plate are investigated such as the value of thermal and mechanical loads, volume fractions of ceramic and metal, and the stiffness coefficients of the foundation.

• Bulletin of the Society of Naval Architects of Korea
• /
• v.19 no.4
• /
• pp.19-29
• /
• 1982

Galerkin's finite element method is applied to a two-dimensional heat convection-diffusion problem arising in the hydrodynamic lubrication of thrust bearings used in naval vessels. A parabolized thermal energy equation for the lubricant, and thermal diffusion equations for both bearing pad and the collar are treated together, with proper juncture conditions on the interface boundaries. it has been known that a numerical instability arises when the classical Galerkin's method, which is equivalent to a centered difference approximation, is applied to a parabolic-type partial differential equation. Probably the simplest remedy for this instability is to use a one-sided finite difference formula for the first derivative term in the finite difference method. However, in the present coupled heat convection-diffusion problem in which the governing equation is parabolized in a subdomain(Lubricant), uniformly stable numerical solutions for a wide range of the Peclet number are obtained in the numerical test based on Galerkin's classical finite element method. In the present numerical convergence errors in several error norms are presented in the first model problem. Additional numerical results for a more realistic bearing lubrication problem are presented for a second numerical model.

• Publications of The Korean Astronomical Society
• /
• v.15 no.spc2
• /
• pp.65-71
• /
• 2000

We have investigated the numerical methods to calculate model atmosphere for the analysis of spectral lines emitted from the sun and stars. Basic equations used in our calculations are radiative transfer, statistical equilibrium and charge-particle conservations. Transfer equation has been solved to get emitting spectral line profile as an initial value problem using Adams-Bashforth-Moulton method with accuracy as high as 12th order. And we have calculated above non linear differential equations simultaneously as a boundary value problem by finite difference method of 3 points approximation through Feautrier elimination scheme. It is found that all computing programs coded by above numerical methods work successfully for our model atmosphere.

• Journal of Mechanical Science and Technology
• /
• v.14 no.9
• /
• pp.1005-1012
• /
• 2000

Numerical optimization techniques combined with a three-dimensional thin-layer Navier-Stokes solver are presented to find an optimum shape of a stator blade in an axial compressor through calculations of single stage rotor-stator flow. Governing differential equations are discretized using an explicit finite difference method and solved by a multi-stage Runge-Kutta scheme. Baldwin-Lomax model is chosen to describe turbulence. A spatially-varying time-step and an implicit residual smoothing are used to accelerate convergence. A steady mixing approach is used to pass information between stator and rotor blades. For numerical optimization, searching direction is found by the steepest decent and conjugate direction methods, and the golden section method is used to determine optimum moving distance along the searching direction. The object of present optimization is to maximize efficiency. An optimum stacking line is found to design a custom-tailored 3-dimensional blade for maximum efficiency with the other parameters fixed.

• Proceedings of the KIEE Conference
• /
• 1989.07a
• /
• pp.418-421
• /
• 1989

A program for numerical analysis of induced lightning surge is developed. The program first converts simultaneous differential equations into simultaneous difference equations for line sections without transition points, and calculates the line voltage and current by solving a determinant. It, then, calculates the line voltage and current at transition points by applying kirhhoffs law. This program is potentially useful in a wide range of applications for investigating the effect on distribution lines of lightning protection equipment such as lightning arresters and overhead ground wires.

• 한국전산유체공학회:학술대회논문집
• /
• 1998.05a
• /
• pp.156-161
• /
• 1998

This describes a numerical method for predicting the incompressible unsteady laminar three-dimensional flows of fluid behaviour with free-surface. The elliptic differential equations governing the flows have been linearized by means of finite-difference approximations, and the resulting equations have been solved via a fully-implicit iterative method. The free-surface is defined by the motion of a set of marker particles and interface behaviour was investigated by way of a 'Lagrangian' technique. Using the GALA concept of Spalding, the conventional mass continuity equation is modified to form a volumetric or bulk-continuity equation. The use of this bulk-continuity relation allows the hydrodynamic variables to be computed over the entire flow domain including both liquid and gas regions. Thus, the free-surface boundary conditions are imposed implicitly and the problem formulation is greatly simplified. The numerical procedure is validated by comparing the predicted results of a periodic standing waves problems with analytic solutions or experimental results from the literature. The results show that this numerical method produces accurate and physically realistic predictions of three-dimensional free-surface flows.

• Proceedings of the Korean Society of Marine Engineers Conference
• /
• 2005.06a
• /
• pp.183-188
• /
• 2005

The effect of heat conduction resistance on laminar film condensation of the pure saturated vapor in forced flow over a flat plate has been investigated as boundary layer solutions. A efficient numerical methods for water are proposed for its solution. The momentum and energy balance equations are reduced to a nonlinear system of ordinary differential equations with four parameters: the Prandtl number, Pr, Modified Jacob number, $Ja^{\ast}/Pr$, defined by an overall temperature difference, a property ratio $\sqrt{P_l{\mu}_l/P_v{\mu}_v}$ and the conjugate parameter ${\zeta}$. The similarity and simplified solutions obtained reveal the effects of the conjugate parameter.