Hua Li¹, Shantanu S. Mulay¹, Simon See²

CMES-Computer Modeling in Engineering & Sciences, Vol.48, No.1, pp. 43-82, 2009, DOI:10.3970/cmes.2009.048.043

Abstract Differential Quadrature (DQ) is one of the efficient derivative approximation techniques but it requires a regular domain with all the points distributed only along straight lines. This severely restricts the DQ while solving the irregular domain problems discretized by the random field nodes. This limitation of the DQ method is overcome in a proposed novel strong-form meshless method, called the random differential quadrature (RDQ) method. The RDQ method extends the applicability of the DQ technique over the irregular or regular domains discretized using the random field nodes by approximating a function value with the fixed… More >

D. L. Young^1,2, C. P. Sun¹, L. H. Shen¹

CMES-Computer Modeling in Engineering & Sciences, Vol.46, No.2, pp. 129-150, 2009, DOI:10.3970/cmes.2009.046.129

Abstract A local differential quadrature (LDQ) method to solve the option-pricing models with stochastic volatilities is proposed. The present LDQ method is a newly developed numerical method which preserves the advantage of high-order numerical solution from the classic differential quadrature (DQ) method. The scheme also overcomes the negative effect of the ill-condition for the resultant full matrix and the sensitivity to the grid distribution. It offers a much better approach for finding the optimal order of polynomial approximation when compared to the conventional DQ method. The option-pricing problem under the stochastic volatilities is an important financial… More >

C. Shu^1,2, H. Ding², K.S. Yeo²

CMES-Computer Modeling in Engineering & Sciences, Vol.7, No.2, pp. 195-206, 2005, DOI:10.3970/cmes.2005.007.195

Abstract Local radial basis function-based differential quadrature (RBF-DQ) method was recently proposed by us. The method is a natural mesh-free approach. It can be regarded as a combination of the conventional differential quadrature (DQ) method with the radial basis functions (RBFs) by means of taking the RBFs as the trial functions in the DQ scheme. With the computed weighting coefficients, the method works in a very similar fashion as conventional finite difference schemes. In this paper, we mainly concentrate on the applications of the method to incompressible flows in the steady and unsteady regions. The multiquadric More >