International Journal of Computational Mathematics http://www.hindawi.com The latest articles from Hindawi Publishing Corporation © 2014 , Hindawi Publishing Corporation . All rights reserved. Solving Operator Equation Based on Expansion Approach Sun, 07 Sep 2014 07:08:56 +0000 http://www.hindawi.com/journals/ijcm/2014/671965/ To date, researchers usually use spectral and pseudospectral methods for only numerical approximation of ordinary and partial differential equations and also based on polynomial basis. But the principal importance of this paper is to develop the expansion approach based on general basis functions (in particular case polynomial basis) for solving general operator equations, wherein the particular cases of our development are integral equations, ordinary differential equations, difference equations, partial differential equations, and fractional differential equations. In other words, this paper presents the expansion approach for solving general operator equations in the form , with respect to boundary condition , where , and are linear, nonlinear, and boundary operators, respectively, related to a suitable Hilbert space, is the domain of approximation, is an arbitrary constant, and is an arbitrary function. Also the other importance of this paper is to introduce the general version of pseudospectral method based on general interpolation problem. Finally some experiments show the accuracy of our development and the error analysis is presented in norm. A. Aminataei, S. Ahmadi-Asl, and M. Pakbaz Copyright © 2014 A. Aminataei et al. All rights reserved. On the Spectrum and Spectral Norms of -Circulant Matrices with Generalized -Horadam Numbers Entries Sun, 31 Aug 2014 10:56:35 +0000 http://www.hindawi.com/journals/ijcm/2014/795175/ This work is concerned with the spectrum and spectral norms of -circulant matrices with generalized -Horadam numbers entries. By using Abel transformation and some identities we obtain an explicit formula for the eigenvalues of them. In addition, a sufficient condition for an -circulant matrix to be normal is presented. Based on the results we obtain the precise value for spectral norms of normal -circulant matrix with generalized -Horadam numbers, which generalize and improve the known results. Lele Liu Copyright © 2014 Lele Liu. All rights reserved. Solving the Generalized Regularized Long Wave Equation Using a Distributed Approximating Functional Method Tue, 12 Aug 2014 12:53:08 +0000 http://www.hindawi.com/journals/ijcm/2014/178024/ The generalized regularized long wave (GRLW) equation is solved numerically by using a distributed approximating functional (DAF) method realized by the regularized Hermite local spectral kernel. Test problems including propagation of single solitons, interaction of two and three solitons, and conservation properties of mass, energy, and momentum of the GRLW equation are discussed to test the efficiency and accuracy of the method. Furthermore, using the Maxwellian initial condition, we show that the number of solitons which are generated can be approximately determined. Comparisons are made between the results of the proposed method, analytical solutions, and numerical methods. It is found that the method under consideration is a viable alternative to existing numerical methods. Edson Pindza and Eben Maré Copyright © 2014 Edson Pindza and Eben Maré. All rights reserved. The Convergence of Geometric Mesh Cubic Spline Finite Difference Scheme for Nonlinear Higher Order Two-Point Boundary Value Problems Wed, 23 Jul 2014 09:30:37 +0000 http://www.hindawi.com/journals/ijcm/2014/527924/ An efficient algorithm for the numerical solution of higher (even) orders two-point nonlinear boundary value problems has been developed. The method is third order accurate and applicable to both singular and nonsingular cases. We have used cubic spline polynomial basis and geometric mesh finite difference technique for the generation of this new scheme. The irreducibility and monotone property of the iteration matrix have been established and the convergence analysis of the proposed method has been discussed. Some numerical experiments have been carried out to demonstrate the computational efficiency in terms of convergence order, maximum absolute errors, and root mean square errors. The numerical results justify the reliability and efficiency of the method in terms of both order and accuracy. Navnit Jha, R. K. Mohanty, and Vinod Chauhan Copyright © 2014 Navnit Jha et al. All rights reserved.