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  1. No Access

    Article

    An Optimal Control Method for Nonlinear Inverse Diffusion Coefficient Problem

    This paper investigates the solution of a parameter identification problem associated with the two-dimensional heat equation with variable diffusion coefficient. The singularity of the diffusion coefficient re...

    Zui-Cha Deng, Y.-C. Hon, Liu Yang in Journal of Optimization Theory and Applications (2014)

  2. No Access

    Article

    Solving the 3D Laplace equation by meshless collocation via harmonic kernels

    This paper solves the Laplace equation Δu = 0 on domains Ω ⊂ ℝ3 by meshless collocation on scattered points of the boundary $\partial\...

    Y. C. Hon, R. Schaback in Advances in Computational Mathematics (2013)

  3. No Access

    Article

    Super quasiperiodic wave solutions and asymptotic analysis for \( \mathcal{N} = 1 \) supersymmetric KdV-type equations

    Based on a general multidimensional Riemann theta function and the super Hirota bilinear form, we extend the Hirota method to construct explicit super quasiperiodic (multiperiodic) wave solutions of ...

    Y. C. Hon, Engui Fan in Theoretical and Mathematical Physics (2011)

  4. No Access

    Article

    Discretized Tikhonov regularization by reproducing kernel Hilbert space for backward heat conduction problem

    In this paper we propose a numerical reconstruction method for solving a backward heat conduction problem. Based on the idea of reproducing kernel approximation, we reconstruct the unknown initial heat distrib...

    Y. C. Hon, Tomoya Takeuchi in Advances in Computational Mathematics (2011)

  5. No Access

    Article

    Solvability of partial differential equations by meshless kernel methods

    This paper first provides a common framework for partial differential equation problems in both strong and weak form by rewriting them as generalized interpolation problems. Then it is proven that any well-pos...

    Y. C. Hon, Robert Schaback in Advances in Computational Mathematics (2008)

  6. No Access

    Article

    Numerical differentiation by radial basis functions approximation

    Based on radial basis functions approximation, we develop in this paper a new com-putational algorithm for numerical differentiation. Under an a priori and an a posteriori choice rules for the regularization para...

    T. Wei, Y. C. Hon in Advances in Computational Mathematics (2007)

  7. No Access

    Chapter and Conference Paper

    A COMPUTATIONAL METHOD FOR SOLVING CAUCHY PROBLEMS OF ELLIPTIC OPERATORS

    In this talk we combine a meshless method of fundamental solution (MFS) with different regularization methods to solve Cauchy problems of elliptic differential operators. The main idea of MFS is to approximate th...

    Y.C. Hon, T. Wei, L. Ling in Computational Methods (2006)

  8. No Access

    Article

    An Adaptive Greedy Algorithm for Solving Large RBF Collocation Problems

    The solution of operator equations with radial basis functions by collocation in scattered points leads to large linear systems which often are nonsparse and ill-conditioned. But one can try to use only a subs...

    Y.C. Hon, R. Schaback, X. Zhou in Numerical Algorithms (2003)

  9. No Access

    Article

    Numerical algorithm for triphasic model of charged and hydrated soft tissues

     This paper devises an efficient numerical algorithm for solving a two-dimensional triphasic model of charged and hydrated soft tissue by using the radial basis functions. The proposed numerical method is appl...

    Y. C. Hon, M. W. Lu, W. M. Xue, X. Zhou in Computational Mechanics (2002)

  10. No Access

    Article

    A new formulation and computation of the triphasic model for mechano-electrochemical mixtures

    From the generalized first law of thermodynamics for an irreversible thermodynamical system, a new set of governing equations for the mixture theory is derived based on the triphasic model for mechano-electro...

    Y. C. Hon, M. W. Lu, W. M. Xue, X. Zhou in Computational Mechanics (1999)

  11. No Access

    Article

    A Multiquadric Interpolation Method for Solving Initial Value Problems

    In this paper, an interpolation method for solving linear differential equations was developed using multiquadric scheme. Unlike most iterative formula, this method provides a global interpolation formula for ...

    Y. C. Hon, X. Z. Mao in Journal of Scientific Computing (1997)

  12. No Access

    Chapter and Conference Paper

    On the Penalty Method of Stokes Equations and Biphasic Mixture Model of Soft Hydrated Tissues

    In conventional penalty methods of Stokes equations and N-S equations the pressure term is introduced into the incompressibility equation with a penalty parameter. This motivation is examined in this paper, an...

    W. M. Xue, A. F. T. Mak, D. T. Huang… in Contemporary Research in Engineering Scien… (1995)