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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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  • 11
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    Scattering data computation for the Zakharov-Shabat system (2015)
    Springer
    In: CALCOLO
    Details
    Publication Date: 2015-11-17
    Description: A numerical method to compute the scattering data for the Zakharov-Shabat system associated to the initial value problem for the nonlinear Schrödinger equation is proposed. The method involves the numerical solution of Volterra integral systems with structured kernels, of structured integral equations in unbounded domains and the identification of coefficients and parameters appearing in monomial-exponential sums. Numerical experiments confirm the effectiveness of the proposed technique.
    Print ISSN: 0008-0624
    Electronic ISSN: 1126-5434
    Topics: Mathematics
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  • 12
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    The first integral method for Wu–Zhang system with conformable time-fractional derivative (2015)
    Springer
    In: CALCOLO
    Details
    Publication Date: 2015-10-28
    Description: In this paper, the first integral method is used to construct exact solutions of the time-fractional Wu–Zhang system. Fractional derivatives are described by conformable fractional derivative. This method is based on the ring theory of commutative algebra. The results obtained confirm that the proposed method is an efficient technique for analytic treatment of a wide variety of nonlinear conformable time-fractional partial differential equations.
    Print ISSN: 0008-0624
    Electronic ISSN: 1126-5434
    Topics: Mathematics
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  • 13
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    A new Legendre operational technique for delay fractional optimal control problems (2015)
    Springer
    In: CALCOLO
    Details
    Publication Date: 2015-10-28
    Description: In this paper, new operational matrices for shifted Legendre orthonormal polynomial are derived. This polynomial is used as a basis function for developing a new numerical technique for the delay fractional optimal control problem. The fractional integral is described in the Riemann–Liouville sense, while the fractional derivative is described in the Caputo sense. The operational matrix of fractional integrals is used together with the Lagrange multiplier method for the constrained extremum in order to minimize the performance index. The problem is then reduced to a problem consists of a system of easily solvable algebraic equations. Three numerical examples of different types of delay fractional optimal control problems are implemented with their approximate solutions for confirming the high accuracy and applicability of the proposed method.
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    Electronic ISSN: 1126-5434
    Topics: Mathematics
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  • 14
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    An exponential spline technique for solving fractional boundary value problem (2015)
    Springer
    In: CALCOLO
    Details
    Publication Date: 2015-10-28
    Description: Differential equations of fractional order are widely used in physics, chemistry as well as engineering fields, this is the main reason that the approximate solution of fractional differential equations becomes a hot topic. In this paper, a numerical scheme for a class of fractional boundary value problems (FBVPs) is presented. In this approach, the FBVPs are expressed in terms of Caputo’s fractional derivative. This scheme is based on exponential spline functions consisting of a polynomial part of degree one and an exponential part. For convergence analysis of this method, it is assumed that the exact solution of fractional boundary value problem belongs to a class of \(C^{6}\) -functions. Numerical examples are considered to illustrate the practical usefulness of this method and comparison show that this scheme is more accurate than the existing method Zahra and Elkholy (Numer Algorithms 59:373–391, 2012 ).
    Print ISSN: 0008-0624
    Electronic ISSN: 1126-5434
    Topics: Mathematics
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  • 15
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    Multi-step Chebyshev spectral collocation method for Volterra integro-differential equations (2015)
    Springer
    In: CALCOLO
    Details
    Publication Date: 2015-10-27
    Description: We investigate multi-step Chebyshev spectral collocation method for Volterra integro-differential equations. We obtain numerical solution Y ( t ) and \(Y'(t)\) to approximate unknown function y ( t ) and its derivative \(y'(t)\) while Y ( t ) and \(Y'(t)\) keep the relation that \(Y'(t)\) is the derivative of Y ( t ). We discuss existence and uniqueness of the solution to corresponding discrete system. We provide convergence analysis for proposed method. Numerical experiments are carried out to confirm theoretical results.
    Print ISSN: 0008-0624
    Electronic ISSN: 1126-5434
    Topics: Mathematics
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  • 16
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    A three-term derivative-free projection method for nonlinear monotone system of equations (2015)
    Springer
    In: CALCOLO
    Details
    Publication Date: 2015-10-14
    Description: In this paper, we propose a three-term conjugate gradient method, which has two attractive properties that the search direction is descent and satisfies the famous D-L conjugacy condition without any line search. Moreover, this new three-term conjugate gradient method can be viewed as a modification of the memoryless BFGS method. By combining this new three-term conjugate gradient method with the projection technique proposed by Solodov and Svailter in 1998, we establish a three-term derivative-free projection method for solving nonlinear monotone system of equations. Due to maintain some nice properties of conjugate gradient method such as the simplicity and the low storage, the proposed projection method is very suitable to solve large-scale nonlinear monotone system of equations. The global convergence and R -linear convergence rate of the proposed projection method are proved under some appropriate conditions. The preliminary numerical results are also given to indicate that the proposed projection method is effective and robust.
    Print ISSN: 0008-0624
    Electronic ISSN: 1126-5434
    Topics: Mathematics
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  • 17
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    Simple yet efficient Newton-like method for systems of nonlinear equations (2015)
    Springer
    In: CALCOLO
    Details
    Publication Date: 2015-10-14
    Description: We present a three-step iterative method of convergence order five for solving systems of nonlinear equations. The methodology is based on Newton’s and Newton-like iterations. Hence, the name Newton-like method. Computational efficiency of the new method is considered and compared with well-known existing methods. Numerical tests are performed on some problems of different nature, which confirm robust and efficient convergence behavior of the proposed technique. Moreover, theoretical results concerning order of convergence and computational efficiency are verified in the numerical problems. It is shown that, in general, the new method is more efficient than the existing counterparts.
    Print ISSN: 0008-0624
    Electronic ISSN: 1126-5434
    Topics: Mathematics
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  • 18
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    On the local convergence of Ehrlich method for numerical computation of polynomial zeros (2015)
    Springer
    In: CALCOLO
    Details
    Publication Date: 2015-09-02
    Description: In this paper, we provide a detailed local convergence analysis of the Ehrlich method for numerical computation of all zeros of a polynomial simultaneously. Our results generalize and improve the results of Kyurkchiev and Tashev (C. R. Acad. Bulg. Sci. 34:1053–1055, 1981 ), Wang and Zhao (Computing 43:187–197, 1989 ) and Tilli (Calcolo 35:3–15, 1998 ).
    Print ISSN: 0008-0624
    Electronic ISSN: 1126-5434
    Topics: Mathematics
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  • 19
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    New hybrid conjugate gradient projection method for the convex constrained equations (2015)
    Springer
    In: CALCOLO
    Details
    Publication Date: 2015-08-06
    Description: Based on the two famous Hestenes–Stiefel and Dai–Yuan conjugate gradient methods, a new hybrid conjugate gradient projection method is proposed for the convex constrained equations. At each iteration, the new method is fully free from any derivative evaluations. Furthermore, the search direction generated by the proposed method satisfies the sufficient descent property, which is independent of the line search. Under the condition that the underlying mapping is continuous and monotone, we establish the global convergence of the new method. Compared with traditional methods for solving such problem, our new method does not require the Lipschitz continuity of the underlying mapping. Some large-scale numerical tests are performed and reported, which show that the proposed method is efficient and promising.
    Print ISSN: 0008-0624
    Electronic ISSN: 1126-5434
    Topics: Mathematics
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  • 20
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    On a functional inequality arising in the analysis of finite-volume methods (2015)
    Springer
    In: CALCOLO
    Details
    Publication Date: 2015-07-28
    Description: We establish a Poincaré–Wirtinger type inequality on some particular domains with a precise estimate of the constant depending only on the geometry of the domain. This type of inequality arises, for instance, in the analysis of finite volume (FV) numerical methods. As an application of our result, we prove uniform a priori bounds for the FV approximate solutions of the heat equation with Ventcell boundary conditions in the natural energy space defined as the set of those functions in \(H^1(\varOmega )\) whose traces belong to \(H^1(\partial \varOmega )\) . The main difficulty here comes from the fact that the approximation is performed on non-polygonal control volumes since the domain itself is non-polygonal.
    Print ISSN: 0008-0624
    Electronic ISSN: 1126-5434
    Topics: Mathematics
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