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| 1 | On-line desalting and carbohydrate analysis for immobilized enzyme hydrolysis of waste cellulosic biomass by column-switching high-performance liquid chromatography显示文摘 | C.Cheng C.S.Chen P.H.Hsieh | | 0，，14： | 1 |
| 2 | A Boundary Meshless Method for Solving Heat Transfer Problems Using the Fourier Transform显示文摘Fourier transform is applied to remove the time-dependent variable in the diffusion equation.Under non-harmonic initial conditions this gives rise to a non-homogeneous Helmholtz equation,which is solved by the method of fundamental solutions and the method of particular solutions.The particular solution of Helmholtz equation is available as shown in[4,15].The approximate solution in frequency domain is then inverted numerically using the inverse Fourier transform algorithm.Complex frequencies are used in order to avoid aliasing phenomena and to allow the computation of the static response.Two numerical examples are given to illustrate the effectiveness of the proposed approach for solving 2-D diffusion equations. | A.Tadeu C.S.Chen J.Antonio Nuno Simoes | 2011 | Advances in Applied Mathematics and Mechanics2011，3，5： | 0 |
| 3 | The Method of Fundamental Solutions for Solving Exterior Axisymmetric Helmholtz Problems with High Wave-Number显示文摘In this paper,we investigate the method of fundamental solutions(MFS)for solving exterior Helmholtz problems with high wave-number in axisymmetric domains.Since the coefficientmatrix in the linear system resulting fromtheMFS approximation has a block circulant structure,it can be solved by the matrix decomposition algorithm and fast Fourier transform for the fast computation of large-scale problems and meanwhile saving computer memory space.Several numerical examples are provided to demonstrate its applicability and efficacy in two and three dimensional domains. | Wen Chen Ji Lin C.S.Chen | 2013 | Advances in Applied Mathematics and Mechanics2013，5，4： | 0 |
| 4 | The Method of Fundamental Solutions for Solving Convection-Diffusion Equations with Variable Coefficients显示文摘A meshless method based on the method of fundamental solutions(MFS)is proposed to solve the time-dependent partial differential equations with variable coefficients.The proposed method combines the time discretization and the onestage MFS for spatial discretization.In contrast to the traditional two-stage process,the one-stage MFS approach is capable of solving a broad spectrum of partial differential equations.The numerical implementation is simple since both closed-form approximate particular solution and fundamental solution are easy to find than the traditional approach.The numerical results show that the one-stage approach is robust and stable. | C.M.Fan C.S.Chen J.Monroe | 2009 | Advances in Applied Mathematics and Mechanics2009，1，2： | 0 |
| 5 | The Recursive Formulation of Particular Solutions for Some Elliptic PDEs with Polynomial Source Functions显示文摘In this paper we develop an efficient meshless method for solving inhomogeneous elliptic partial differential equations.We first approximate the source function by Chebyshev polynomials.We then focus on how to find a polynomial particular solution when the source function is a polynomial.Through the principle of the method of undetermined coefficients and a proper arrangement of the terms for the polynomial particular solution to be determined,the coefficients of the particular solution satisfy a triangular system of linear algebraic equations.Explicit recursive formulas for the coefficients of the particular solutions are derived for different types of elliptic PDEs.The method is further incorporated into the method of fundamental solutions for solving inhomogeneous elliptic PDEs.Numerical results show that our approach is efficient and accurate. | J.Ding H.Y.Tian C.S.Chen | 2009 | Communications in Computational Physics2009，5，5： | 0 |
| 6 | A Revisit on the Derivation of the Particular Solution for the Differential Operator ∆^(2) ± λ^(2)显示文摘In this paper,we applied the polyharmonic splines as the basis functions to derive particular solutions for the differential operator ∆^(2) ± λ^(2).Similar to the derivation of fundamental solutions,it is non-trivial to derive particular solutions for higher order differential operators.In this paper,we provide a simple algebraic factorization approach to derive particular solutions for these types of differential operators in 2D and 3D.The main focus of this paper is its simplicity in the sense that minimal mathematical background is required for numerically solving higher order partial differential equations such as thin plate vibration.Three numerical examples in both 2D and 3D are given to validate particular solutions we derived. | Guangming Yao C.S.Chen Chia Cheng Tsai | 2009 | Advances in Applied Mathematics and Mechanics2009，1，6： | 0 |
| 7 | Preface Special Issue for SCPDE08: Numerical Methods and Analysis for PDEs and Inverse Problems显示文摘The Third International Conference on Scientific Computing and Partial Differential Equations(SCPDE)was held from December 8 to December 12,2008 at China Hong Kong Baptist University.It was a sequel to similar conferences held in Hong Kong region(2002 and 2005).The conference aims to promote research interests in scientific computation.In SCPDE 2008,there were 118 participants from seventeen countries and regions participated in the conference.The Programme included seventeen plenary addresses,thirty invited talks,twenty five contributed talks and seven poster presentations. | C.S.Chen Ming-Chih Lai Leevan Ling Jichun Li Masahiro Yamamoto | 2009 | Advances in Applied Mathematics and Mechanics2009，1，6： | 0 |
| 8 | Local RBF Algorithms for Elliptic Boundary Value Problems in Annular Domains显示文摘A local radial basis function method(LRBF)is applied for the solution of boundary value problems in annular domains governed by the Poisson equation,the inhomogeneous biharmonic equation and the inhomogeneous Cauchy-Navier equations of elasticity.By appropriately choosing the collocation points we obtain linear systems in which the coefficient matrices possess block sparse circulant structures and which can be solved efficiently using matrix decomposition algorithms(MDAs)and fast Fourier transforms(FFTs).The MDAs used are appropriately modified to take into account the sparsity of the arrays involved in the discretization.The leave-one-out cross validation(LOOCV)algorithm is employed to obtain a suitable value for the shape parameter in the radial basis functions(RBFs)used.The selection of the nearest centres for each local influence domain is carried out using a modification of the kdtree algorithm.In several numerical experiments,it is demonstrated that the proposed algorithm is both accurate and capable of solving large scale problems. | C.S.Chen Andreas Karageorghis | 2019 | Communications in Computational Physics2019，25，1： | 0 |
| 9 | A Novel Method for Solving Time-Dependent 2D Advection-Diffusion-Reaction Equations to Model Transfer in Nonlinear Anisotropic Media显示文摘This paper presents a new numerical technique for solving initial and bound-ary value problems with unsteady strongly nonlinear advection diffusion reaction(ADR)equations.The method is based on the use of the radial basis functions(RBF)for the approximation space of the solution.The Crank-Nicolson scheme is used for approximation in time.This results in a sequence of stationary nonlinear ADR equations.The equations are solved sequentially at each time step using the proposed semi-analytical technique based on the RBFs.The approximate solution is sought in the form of the analytical expansion over basis functions and contains free parameters.The basis functions are constructed in such a way that the expansion satisfies the boundary conditions of the problem for any choice of the free parameters.The free parameters are determined by substitution of the expansion in the equation and collocation in the solution domain.In the case of a nonlinear equation,we use the well-known procedure of quasilinearization.This transforms the original equation into a sequence of the linear ones on each time layer.The numerical examples confirm the high accuracy and robustness of the proposed numerical scheme. | Ji Lin Sergiy Reutskiy C.S.Chen Jun Lu | 2019 | Communications in Computational Physics2019，26，6： | 0 |
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