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  • Articles  (41)
  • 2015-2019  (41)
  • 2015  (41)
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  • Articles  (41)
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  • 2015-2019  (41)
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  • 1
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    Norm–based approximation in E-[0,1] convex multi-objective programming (2015)
    Springer
    In: CALCOLO
    Details
    Publication Date: 2015-12-30
    Description: This paper addresses the problem of capturing nondominated points on non-convex pareto frontier, which are encountered in E-[0,1] convex multi-objective programming problems. We use E-[0,1] map to transfer non-convex pareto frontier to convex pareto frontier, then An algorithm to find a piecewise linear approximation of the nondominated set of convex pareto frontier are applied. Finally, the inverse map of E-[0,1] is used to get the nondominated set of non-convex pareto frontier.
    Print ISSN: 0008-0624
    Electronic ISSN: 1126-5434
    Topics: Mathematics
    Published by Springer
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  • 2
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    A unified approach to non-polynomial B-spline curves based on a novel variant of the polar form (2015)
    Springer
    In: CALCOLO
    Details
    Publication Date: 2015-12-23
    Description: We develop a general, unified theory of splines for a wide collection of spline spaces, including trigonometric splines, hyperbolic splines, and special Müntz spaces of splines by invoking a novel variant of the homogeneous polar form where we alter the diagonal property. Using this polar form, we derive de Boor type recursive algorithms for evaluation and differentiation. We also show that standard knot insertion procedures such as Boehm’s algorithm and the Oslo algorithm readily extend to these general spline spaces. In addition, for these spaces we construct compactly supported B-spline basis functions with simple two term recurrences for evaluation and differentiation, and we show that these B-spline basis functions form a partition of unity, have curvilinear precision, and satisfy a dual functional property and a Marsden identity.
    Print ISSN: 0008-0624
    Electronic ISSN: 1126-5434
    Topics: Mathematics
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  • 3
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    Error bounds for linear complementarity problems of QN -matrices (2015)
    Springer
    In: CALCOLO
    Details
    Publication Date: 2015-12-20
    Description: We give error bounds for linear complementarity problem when the matrix involved belongs to the class of quasi-Nekrasov ( QN -) matrices including Nekrasov matrices. The obtained bounds can improve considerably other previous bounds.
    Print ISSN: 0008-0624
    Electronic ISSN: 1126-5434
    Topics: Mathematics
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  • 4
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    An efficient numerical algorithm based on Haar wavelet for solving a class of linear and nonlinear nonlocal boundary-value problems (2015)
    Springer
    In: CALCOLO
    Details
    Publication Date: 2015-12-15
    Description: Based on Haar wavelet a new numerical method for the solution of a class of nth-order boundary-value problems (BVPs) with nonlocal boundary conditions is proposed. This new method is an extension of the Haar wavelet method (Siraj-ul-Islam et al. in Math Comput Model 50:1577–1590, 2010 ; Int J Therm Sci 50:686–697, 2011 ) from BVPs with local boundary conditions to BVPs with a class of nonlocal boundary conditions. A major advantage of the proposed method is that it is applicable to both linear and nonlinear BVPs. The method is tested on BVPs of third- and fourth-order. The numerical results are compared with an existing method in the literature and analytical solutions. The numerical experiments demonstrate the accuracy and efficiency of the proposed method.
    Print ISSN: 0008-0624
    Electronic ISSN: 1126-5434
    Topics: Mathematics
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  • 5
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    Spectral discretization of an unsteady flow through a porous solid (2015)
    Springer
    In: CALCOLO
    Details
    Publication Date: 2015-12-15
    Description: We consider the non stationary flow of a viscous incompressible fluid in a rigid homogeneous porous medium provided with mixed boundary conditions. Since the boundary pressure can present high variations, the permeability of the medium also depends on the pressure, so that the problem is nonlinear. We propose a discretization of this equation that combines Euler’s implicit scheme in time and spectral methods in space. We prove optimal a priori error estimates and present some numerical experiments which confirm the interest of the discretization.
    Print ISSN: 0008-0624
    Electronic ISSN: 1126-5434
    Topics: Mathematics
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  • 6
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    A Jacobi–Davidson type method for computing real eigenvalues of the quadratic eigenvalue problem (2015)
    Springer
    In: CALCOLO
    Details
    Publication Date: 2015-12-14
    Description: This paper presents a new Jacobi–Davidson type method to compute several real eigenvalues of the Hermitian quadratic eigenvalue problem. This method uses a simple index to sort the eigenvalues of the projected quadratic eigenvalue problem and extracts the approximate eigenvectors for the quadratic eigenvalue problem with the eigenvectors of the projected quadratic eigenvalue problem corresponding to the eigenvalues with the smallest indices. Numerical examples show that our method is effective and efficient to compute real eigenvalues of the Hermitian quadratic eigenvalue problem.
    Print ISSN: 0008-0624
    Electronic ISSN: 1126-5434
    Topics: Mathematics
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  • 7
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    Mortar finite element discretization of the time dependent nonlinear Darcy’s equations (2015)
    Springer
    In: CALCOLO
    Details
    Publication Date: 2015-12-12
    Description: We consider the non stationary flow of a viscous incompressible fluid in a rigid nonhomogeneous porous medium provided with mixed boundary conditions. Since the medium is nonhomogeneous, its permeability is only piecewise continuous. We are thus led to use the mortar method to handle these discontinuities. We propose a space and time discretization of the full system. We prove optimal a priori error estimates, which confirms the interest of the discretization.
    Print ISSN: 0008-0624
    Electronic ISSN: 1126-5434
    Topics: Mathematics
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  • 8
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    Iterative method for solving nonlinear singular problems (2015)
    Springer
    In: CALCOLO
    Details
    Publication Date: 2015-12-12
    Description: The aim of our work is to present a method ( p -factor method) for solving nonlinear equations of the form $$\begin{aligned} F(x)=0, \quad F:\mathbb {R}^n\rightarrow \mathbb {R}^m, \end{aligned}$$ in singular (irregular) case, i.e. when the matrix \(F'(x)\) is singular at an initial point \(x_0\) of an iterative sequence \(\{x_k\}\) , \(k=1,2,\ldots \) We investigate conditions that have to be fulfilled at the initial point \(x_0\) to obtain the existence of solution of nonlinear equation \(F(x)=0\) , prove convergence of the presented p -factor method and give estimation of convergence rate for this method.
    Print ISSN: 0008-0624
    Electronic ISSN: 1126-5434
    Topics: Mathematics
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  • 9
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    A Legendre–Gauss–Radau spectral collocation method for first order nonlinear delay differential equations (2015)
    Springer
    In: CALCOLO
    Details
    Publication Date: 2015-12-12
    Description: In this paper, we introduce a single-step Legendre–Gauss–Radau spectral collocation method for solving the first order nonlinear delay differential equations with variable delay, and analyze its convergence. We also propose two fast and efficient algorithms for the single-step scheme and apply them to the multiple interval case. Numerical results show that the suggested algorithms enjoy high order accuracy.
    Print ISSN: 0008-0624
    Electronic ISSN: 1126-5434
    Topics: Mathematics
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  • 10
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    Ball convergence of a sixth order iterative method with one parameter for solving equations under weak conditions (2015)
    Springer
    In: CALCOLO
    Details
    Publication Date: 2015-11-24
    Description: We present a local convergence analysis of a sixth order iterative method for approximate a locally unique solution of an equation defined on the real line. Earlier studies such as Sharma et al. (Appl Math Comput 190:111–115, 2007 ) have shown convergence of these methods under hypotheses up to the fifth derivative of the function although only the first derivative appears in the method. In this study we expand the applicability of these methods using only hypotheses up to the first derivative of the function. Numerical examples are also presented in this study.
    Print ISSN: 0008-0624
    Electronic ISSN: 1126-5434
    Topics: Mathematics
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