Scielo RSS <![CDATA[Computational & Applied Mathematics]]> vol. 31 num. 1 lang. en <![CDATA[SciELO Logo]]> <![CDATA[<b>An integrable decomposition of the Manakov equation</b>]]> An integrable decomposition of the Manakov equation is presented. A pair of new finite-dimensional integrable Hamiltonian systems which constitute the integrable decomposition of the Manakov equation are obtained. Mathematical subject classification: 37K10. <![CDATA[<b>A stabilized finite element method to pseudoplastic flow governed by the Sisko relation</b>]]> In this work, a consistent stabilized mixed finite element formulation for incompressible pseudoplastic fluid flows governed by the Sisko constitutive equation is mathematically analysed. This formulation is constructed by adding least-squares of the governing equations and of the incompressibility constraint, with discontinuous pressure approximations, allowing the use of same order interpolations for the velocity and the pressure. Numerical results are presented to confirm the mathematical stability analysis. Mathematical subject classification: Primary: 65M60; Secondary: 65N30. <![CDATA[<b>Numerical solution of the variational PDEs arising in optimal control theory</b>]]> An iterative method based on Picard's approach to ODEs' initial-value problems is proposed to solve first-order quasilinear PDEs with matrix-valued unknowns, in particular, the recently discovered variational PDEs for the missing boundary values in Hamilton equations of optimal control. As illustrations the iterative numerical solutions are checked against the analytical solutions to some examples arising from optimal control problems for nonlinear systems and regular Lagrangians in finite dimension, and against the numerical solution obtained through standard mathematical software. An application to the (n + 1)-dimensional variational PDEs associated with the n-dimensional finite-horizon time-variant linear-quadratic problem is discussed, due to the key role the LQR plays in two-degrees-of freedom control strategies for nonlinear systems with generalized costs. Mathematical subject classification: Primary: 35F30; Secondary: 93C10. <![CDATA[<b>The global convergence of a descent PRP conjugate gradient method</b>]]> Recently, Yu and Guan proposed a modified PRP method (called DPRP method) which can generate sufficient descent directions for the objective function. They established the global convergence of the DPRP method based on the assumption that stepsize is bounded away from zero. In this paper, without the requirement of the positive lower bound of the stepsize, we prove that the DPRP method is globally convergent with a modified strong Wolfe line search. Moreover, we establish the global convergence of the DPRP method with a Armijo-type line search. The numerical results show that the proposed algorithms are efficient. Mathematical subject classification: Primary: 90C30; Secondary: 65K05. <![CDATA[<b>Sharpness of Muqattash-Yahdi problem</b>]]> Let ψ denote the psi (or digamma) function. We determine the values of theparameters p, q and r such that ψ(n) ≈ ln(n + p) - <img border=0 width=32 height=32 src="../../../../../img/revistas/cam/v31n1/a05img01.jpg" align=absmiddle> is the best approximations. Also, we present closer bounds for psi function, which sharpens some known results due to Muqattash and Yahdi, Qi and Guo, and Mortici. Mathematical subject classification: 33B15, 26D15. <![CDATA[<b>On a linearisation method for Reiner-Rivlin swirling flow</b>]]> The steady flow of a Reiner-Rivlin fluid with Joule heating and viscous dissipationis studied. We present a novel technique for accelerating the convergence of the spectral-homotopy analysis method. Solutions of the nonlinear momentum and energy equations are obtained using the improved spectral homotopy analysis method. Solutions were also generated using the spectral-homotopy analysis method and benchmarked against results in the literature. Mathematical subject classification: Primary: 76A05, 76N05; Secondary: 76M25. <![CDATA[<b>Chebyshev polynomials for solving two dimensional linear and nonlinear integral equations of the second kind</b>]]> In this paper, an efficient method is presented for solving two dimensional Fredholm and Volterra integral equations of the second kind. Chebyshev polynomials are applied to approximate a solution for these integral equations. This method transforms the integral equation to algebraic equations with unknown Chebyshev coefficients. The high accuracy of this method is verified through some numerical examples. Mathematical subject classification: 65R20, 41A50, 41A55, 65M70. <![CDATA[<b>A new approach for data transmission system on topological surfaces</b>]]> This work introduces a new data transmission system in which the main blocks, coding, modulation and channel are designed on a Riemannian manifolds. An intrinsic algebraic structure to the manifolds (surface), the homology group will be used to compose an error corrector code, a partition on the surface extracted from the embedding of a graph, which will compose the modulation design, and the channel design is the result of an association rule applied to the embedded graph. Mathematical subject classification: Primary: 06B10; Secondary: 06D05. <![CDATA[<b>Fundamental solution in the theory of micropolar thermoelastic diffusion with voids</b>]]> In the present article, we construct the fundamental solution of system of differential equations in the theory of micropolar thermoelastic diffusion with voids in case of steady oscillations in terms of elementary functions. Some basic properties of the fundamental solution are also established. Some special cases are also discussed. Mathematical subject classification: 74Bxx, 74Fxx, 74Hxx. <![CDATA[<b>A block by block method with Romberg quadrature for the system of Urysohn type Volterra integral equations</b>]]> In this paper, we propose an efficient numerical method for solving systems of linear and nonlinear integral equations of the first and second kinds, which avoids the need for special starting values. The method has also the advantages of simplicity of application and at least six order of convergence. A convergence analysis is given and accuracy of the method is clarified by numerical examples. Mathematical subject classification: 65R20. <![CDATA[<b>A sensitivity result for quadratic semidefinite programs with an application to a sequential quadratic semidefinite programming algorithm</b>]]> In this short note a sensitivity result for quadratic semidefinite programming is presented under a weak form of second order sufficient condition. Based on this result, also the local convergence of a sequential quadratic semidefinite programming algorithm extends to this weak second order sufficient condition. Mathematical subject classification: 90C22, 90C30, 90C31, 90C55.