• Title/Summary/Keyword: differential difference equations

Search Result 217, Processing Time 0.029 seconds

Convergence of nonlinear algorithms

  • Lee, Young-S.;Simeon Reich
    • Journal of the Korean Mathematical Society
    • /
    • v.32 no.1
    • /
    • pp.115-139
    • /
    • 1995
  • Our purpose in this paper is to prove a new version of the nonlinear Chernoff theorem and to discuss the equivalence between resolvent consistency and converge nce for nonlinear algorithms acting on different Banach spaces. Such results are useful in the numerical treatment of partial differential equations via difference schemes.

  • PDF

Dynamic Analysis of MLS Difference Method using First Order Differential Approximation (1차 미분 근사를 이용한 MLS차분법의 동적해석)

  • Kim, Kyeong-Hwan;Yoon, Young-Cheol;Lee, Sang-Ho
    • Journal of the Computational Structural Engineering Institute of Korea
    • /
    • v.31 no.6
    • /
    • pp.331-337
    • /
    • 2018
  • This paper presents dynamic algorithm of the MLS(moving least squares) difference method using first order differential Approximation. The governing equations are only discretized by the first order MLS derivative approximation. The system equation consists of an assembly of the approximate function, so the shape of system equation is similar to FEM(finite element method). The CDM(central difference method) is used for time integration of dynamic equilibrium equation. The natural frequency analyses of the MLS difference method and FEM are performed, and two analysis results are compared. Also, the accuracy of the proposed numerical method is verified by displaying the dynamic analysis results together with the results by the existing second order differential approximation. In the process of assembling the first order MLS derivative approximation, the oscillation error was suppressed and the stress distribution was interpreted as relatively uniform.

RECTANGULAR DOMAIN DECOMPOSITION METHOD FOR PARABOLIC PROBLEMS

  • Jun, Youn-Bae;Mai, Tsun-Zee
    • The Pure and Applied Mathematics
    • /
    • v.13 no.4 s.34
    • /
    • pp.281-294
    • /
    • 2006
  • Many partial differential equations defined on a rectangular domain can be solved numerically by using a domain decomposition method. The most commonly used decompositions are the domain being decomposed in stripwise and rectangular way. Theories for non-overlapping domain decomposition(in which two adjacent subdomains share an interface) were often focused on the stripwise decomposition and claimed that extensions could be made to the rectangular decomposition without further discussions. In this paper we focus on the comparisons of the two ways of decompositions. We consider the unconditionally stable scheme, the MIP algorithm, for solving parabolic partial differential equations. The SOR iterative method is used in the MIP algorithm. Even though the theories are the same but the performances are different. We found out that the stripwise decomposition has better performance.

  • PDF

Impact of Receiver on In-Band Crosstalk-Induced Penalties in Differentially Phase-Modulated Signals

  • Hu, Qikai;Kim, Hoon;Kim, Chul Han
    • Journal of the Optical Society of Korea
    • /
    • v.20 no.2
    • /
    • pp.223-227
    • /
    • 2016
  • The impact of optical receiver configuration on in-band crosstalk-induced penalty has been investigated in both theoretical and experimental analyses, for differential phase-shift keying (DPSK) and differential quadrature phase-shift keying (DQPSK) signals. Previously it has been shown that DPSK signals are ~6 dB more tolerant to in-band crosstalk than on-off keying (OOK) signals. However, we find that the tolerance difference between the two signals is reduced to ~3 dB when the decision threshold of the receiver is optimized to minimize the bit-error rate for each signal. Then we derive simple equations for the in-band crosstalk-induced penalty in DPSK and DQPSK signals with two different optical receiver configurations: balanced and single-ended direct-detection receivers. We confirm that the penalties obtained from our simple equations agree well with the measured results.

Development of 3-Dimensional Simulator for a Biped Robot (이족 보행로봇의 3차원 모의실험기 개발)

  • Noh, Kyung-Kon;Kim, Jin-Geol;Huh, Uk-Youl
    • Proceedings of the KIEE Conference
    • /
    • 2004.07d
    • /
    • pp.2438-2440
    • /
    • 2004
  • This study is concerned with development of 3-Dimensional simulator of a biped robot that has a prismatic balancing weight or a revolute balancing weight. The dynamic stability equation of a biped robot which have a prismatic balancing weight is conditional linear but a walking robot's stability equation with a revolute balancing weight is nonlinear. To get a stable gait of a biped robot, stabilization equations with ZMP (Zero Moment Point) are modeled as non-homogeneous second order differential equations for each balancing weight type. A trajectory of balancing weight can be directly calculated with the FDM (Finite Difference Method) solution of the linearized differential equation. In this paper, the 3-Dimensional graphic simulator is programmed to get and calculate the desired ZMP and the actual ZMP. Walking of 4 steps was simulated and verified. This balancing system will be applied to a biped humanoid robot, which consist Begs and upper body, at future work.

  • PDF

Large Amplitude Oscillations in a Hanging Cable and Suspension Bridge: Some New Connections with Nonlinear Analysis (케이블과 현수교 다리에서 일어나는 진폭이 큰 진동에 대한 연구)

  • Oh Hye-Young
    • Journal of the Korea Computer Industry Society
    • /
    • v.7 no.1
    • /
    • pp.33-38
    • /
    • 2006
  • The motions of suspension bridge as well as hanging cable are governed by nonlinear partial differential equations. Nonlinearity gives rise to a large amplitude oscillation. We use finite difference methods to compute periodic solutions to the torsional partial differential equations. We use the one-noded forcing term and a slight perturbation in the forcing term.

  • PDF

On a new fourth order self-adaptive time integration algorithm

  • Zhong, Wanxie;Zhu, Jianping
    • Structural Engineering and Mechanics
    • /
    • v.4 no.6
    • /
    • pp.589-600
    • /
    • 1996
  • An explicit 4th order time integration scheme for solving the convection-diffusion equation is discussed in this paper. A system of ordinary differential equations are derived first by discretizing the spatial derivatives of the relevant PDE using the finite difference method. The integration of the ODEs is then carried out using a 4th order scheme and a self-adaptive technique based on the spatial grid spacing. For a non-uniform spatial grid, different time step sizes are used for the integration of the ODEs defined at different spatial points, which improves the computational efficiency significantly. A numerical example is also discussed in the paper to demonstrate the implementation and effectiveness of the method.

Application of Bootstrap Method to Primary Model of Microbial Food Quality Change

  • Lee, Dong-Sun;Park, Jin-Pyo
    • Food Science and Biotechnology
    • /
    • v.17 no.6
    • /
    • pp.1352-1356
    • /
    • 2008
  • Bootstrap method, a computer-intensive statistical technique to estimate the distribution of a statistic was applied to deal with uncertainty and variability of the experimental data in stochastic prediction modeling of microbial growth on a chill-stored food. Three different bootstrapping methods for the curve-fitting to the microbial count data were compared in determining the parameters of Baranyi and Roberts growth model: nonlinear regression to static version function with resampling residuals onto all the experimental microbial count data; static version regression onto mean counts at sampling times; dynamic version fitting of differential equations onto the bootstrapped mean counts. All the methods outputted almost same mean values of the parameters with difference in their distribution. Parameter search according to the dynamic form of differential equations resulted in the largest distribution of the model parameters but produced the confidence interval of the predicted microbial count close to those of nonlinear regression of static equation.

HYBRID DIFFERENCE SCHEMES FOR A SYSTEM OF SINGULARLY PERTURBED CONVECTION-DIFFUSION EQUATIONS

  • Priyadharshini, R.Mythili;Ramanujam, N.;Tamilselvan, A.
    • Journal of applied mathematics & informatics
    • /
    • v.27 no.5_6
    • /
    • pp.1001-1015
    • /
    • 2009
  • In this paper, two hybrid difference schemes on the Shishkin mesh are constructed for solving a weakly coupled system of two singularly perturbed convection-diffusion second order ordinary differential equations with a small parameter multiplying the highest derivative. We prove that the schemes are almost second order convergence in the supremum norm independent of the diffusion parameter. Error bounds for the numerical solution and its derivative are established. Numerical results are provided to illustrate the theoretical results.

  • PDF