Home / Advanced Search

  • Title/Keywords

  • Author/Affliations

  • Journal

  • Article Type

  • Start Year

  • End Year

Update SearchingClear
  • Articles
  • Online
Search Results (18)
  • Open Access


    Wavelet operational matrix method for solving fractional integral and differential equations of Bratu-type

    Lifeng Wang1, Yunpeng Ma1, Zhijun Meng1, Jun Huang1

    CMES-Computer Modeling in Engineering & Sciences, Vol.92, No.4, pp. 353-368, 2013, DOI:10.3970/cmes.2013.092.353

    Abstract In this paper, a wavelet operational matrix method based on the second kind Chebyshev wavelet is proposed to solve the fractional integral and differential equations of Bratu-type. The second kind Chebyshev wavelet operational matrix of fractional order integration is derived. A truncated second kind Chebyshev wavelet series together with the wavelet operational matrix is utilized to reduce the fractional integral and differential equations of Bratu-type to a system of nonlinear algebraic equations. The convergence and the error analysis of the method are also given. Two examples are included to verify the validity and applicability of More >

  • Open Access


    Numerical solution of nonlinear fractional integral differential equations by using the second kind Chebyshev wavelets

    Yiming Chen1, Lu Sun1, Xuan Li1, Xiaohong Fu1

    CMES-Computer Modeling in Engineering & Sciences, Vol.90, No.5, pp. 359-378, 2013, DOI:10.3970/cmes.2013.090.359

    Abstract By using the differential operator matrix and the product operation matrix of the second kind Chebyshev wavelets, a class of nonlinear fractional integral-differential equations is transformed into nonlinear algebraic equations, which makes the solution process and calculation more simple. At the same time, the maximum absolute error is obtained through error analysis. It also can be used under the condition that no exact solution exists. Numerical examples verify the validity of the proposed method. More >

  • Open Access


    Numerical Solution of Space-Time Fractional Convection-Diffusion Equations with Variable Coefficients Using Haar Wavelets

    Jinxia Wei1, Yiming Chen1, Baofeng Li2, Mingxu Yi1

    CMES-Computer Modeling in Engineering & Sciences, Vol.89, No.6, pp. 481-495, 2012, DOI:10.3970/cmes.2012.089.481

    Abstract In this paper, we present a computational method for solving a class of space-time fractional convection-diffusion equations with variable coefficients which is based on the Haar wavelets operational matrix of fractional order differentiation. Haar wavelets method is used because its computation is sample as it converts the original problem into Sylvester equation. Error analysis is given that shows efficiency of the method. Finally, a numerical example shows the implementation and accuracy of the approach. More >

  • Open Access


    Error Analysis of Trefftz Methods for Laplace's Equations and Its Applications

    Z. C. Li2, T. T. Lu3, H. T. Huang4, A. H.-D. Cheng5

    CMES-Computer Modeling in Engineering & Sciences, Vol.52, No.1, pp. 39-82, 2009, DOI:10.3970/cmes.2009.052.039

    Abstract For Laplace's equation and other homogeneous elliptic equations, when the particular and fundamental solutions can be found, we may choose their linear combination as the admissible functions, and obtain the expansion coefficients by satisfying the boundary conditions only. This is known as the Trefftz method (TM) (or boundary approximation methods). Since the TM is a meshless method, it has drawn great attention of researchers in recent years, and Inter. Workshops of TM and MFS (i.e., the method of fundamental solutions). A number of efficient algorithms, such the collocation algorithms, Lagrange multiplier methods, etc., have been More >

  • Open Access


    Application of Residual Correction Method on Error Analysis of Numerical Solution on the non-Fourier Fin Problem

    Hsiang-Wen Tang, Cha’o-Kung Chen1, Chen-Yu Chiang

    CMES-Computer Modeling in Engineering & Sciences, Vol.65, No.1, pp. 95-106, 2010, DOI:10.3970/cmes.2010.065.095

    Abstract Up to now, solving some nonlinear differential equations is still a challenge to many scholars, by either numerical or theoretical methods. In this paper, the method of the maximum principle applied on differential equations incorporating the Residual Correction Method is brought up and utilized to obtain the upper and lower approximate solutions of nonlinear heat transfer problem of the non-Fourier fin. Under the fundamental of the maximum principle, the monotonic residual relations of the partial differential governing equation are established first. Then, the finite difference method is applied to discretize the equation, converting the differential More >

  • Open Access


    Particle Methods for a 1D Elastic Model Problem: Error Analysis and Development of a Second-Order Accurate Formulation

    D. Asprone1, F. Auricchio2, G. Manfredi1, A. Prota1, A. Reali2, G. Sangalli3

    CMES-Computer Modeling in Engineering & Sciences, Vol.62, No.1, pp. 1-22, 2010, DOI:10.3970/cmes.2010.062.001

    Abstract Particle methods represent some of the most investigated meshless approaches, applied to numerical problems, ranging from solid mechanics to fluid-dynamics and thermo-dynamics. The objective of the present paper is to analyze some of the proposed particle formulations in one dimension, investigating in particular how the different approaches address second derivative approximation. With respect to this issue, a rigorous analysis of the error is conducted and a novel second-order accurate formulation is proposed. Hence, as a benchmark, three numerical experiments are carried out on the investigated formulations, dealing respectively with the approximation of the second derivative More >

  • Open Access


    Error Analysis of Various Basis Functions Used in BEM Solution of Acoustic Scattering

    B. Chandrasekhar1

    CMES-Computer Modeling in Engineering & Sciences, Vol.56, No.3, pp. 211-230, 2010, DOI:10.3970/cmes.2010.056.211

    Abstract In this work, various basis functions used in the Method of Moments or Boundary Element (MoM/BEM) solution of acoustic scattering problems are compared with each other for their performance. Single layer formulation of the rigid bodies is considered in comparison of the solutions. Geometry of a scatterer is descritized using triangular patch modeling and basis functions are defined on triangular patches, edges and nodes for three different solutions. Far field scattering cross sections for different frequencies of incident acoustic wave are compared with the closed form solutions. Also, the errors of the solutions using these More >

  • Open Access


    Error Reduction in Gauss-Jacobi-Nyström Quadraturefor Fredholm Integral Equations of the Second Kind

    M. A. Kelmanson1 and M. C. Tenwick1

    CMES-Computer Modeling in Engineering & Sciences, Vol.55, No.2, pp. 191-210, 2010, DOI:10.3970/cmes.2010.055.191

    Abstract A method is presented for improving the accuracy of the widely used Gauss-Legendre Nyström method for determining approximate solutions of Fredholm integral equations of the second kind on finite intervals. The authors' recent continuous-kernel approach is generalised in order to accommodate kernels that are either singular or of limited continuous differentiability at a finite number of points within the interval of integration. This is achieved by developing a Gauss-Jacobi Nyström method that moreover includes a mean-value estimate of the truncation error of the Hermite interpolation on which the quadrature rule is based, making it particularly More >

Displaying 11-20 on page 2 of 18. Per Page