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article

An equivalence lemma for a class of fuzzy implicit integro-differential equations

Masoumeh Zeinali, Sedaghat Shahmorad

Journal of Computational and Applied Mathematics > 2018 > 327 > Complete > 388-399

In the current paper, an equivalence lemma is proposed which converts a second order implicit form of nonlinear fuzzy Volterra integro-differential equation to four different kinds of nonlinear integral equations based on kind of GH-differentiability of the first and second derivatives. Finally, some examples are given to illustrate the theoretical results.

article

Numerical integration based on hyperfunction theory

Hidenori Ogata, Hiroshi Hirayama

Journal of Computational and Applied Mathematics > 2018 > 327 > Complete > 243-259

In this paper, we propose an application of hyperfunction theory to numerical integration. Hyperfunction theory is a generalized version of function theory where functions with singularities such as poles, discontinuities and delta impulses are expressed in terms of complex analytic functions. This feature of hyperfunction theory allows us to construct a numerical integration method for analytic functions...

article

A modified Lavrentiev iterative regularization method for analytic continuation

Xiangtuan Xiong, Qiang Cheng

Journal of Computational and Applied Mathematics > 2018 > 327 > Complete > 127-140

We consider the problem of numerical analytic continuation of an analytic function f ( z ) = f ( x + i y ) on a strip domain Ω + = { z = x + i y ∈ C | x ∈ R , 0 < y < y 0 } , where the data is given approximately only on the line y = 0 . This is a severely ill-posed problem. Motivated by the advantage of iterative methods for solving ill-posed problems, we propose a new...

article

The direct method of lines for elliptic problems in star-shaped domains

Zhizhang Wu, Zhongyi Huang, Wei-Cheng Wang, Yi Yang

Journal of Computational and Applied Mathematics > 2018 > 327 > Complete > 350-361

In this paper, we generalize the direct method of lines for elliptic problems in star-shaped domains. We assume that the boundary of the star-shaped domain is a closed Lipschitz curve that can be parameterized by the angular variable, so that an appropriate transformation of coordinates can be introduced. Then the elliptic problem is reduced to a variational–differential problem on a semi-infinite...

article

An algorithm for finding intersection between ball B-spline curves

Qian Fu, Zhongke Wu, Xingce Wang, Mingquan Zhou, more

Journal of Computational and Applied Mathematics > 2018 > 327 > Complete > 260-273

A ball B-spline curve (BBSC) is a skeleton based solid model representation, which consists of a B-spline curve and a B-spline function serving as the (varying) radius of a ball moving along the B-spline curve. The surface shape specified by the BBSC is the envelope of the moving ball and thus the BBSC is very suitable for representing vascular shapes. To apply this good representation in various...

article

Complex-step derivative approximation in noisy environment

Filip Nikolovski, Irena Stojkovska

Journal of Computational and Applied Mathematics > 2018 > 327 > Complete > 64-78

The complex-step derivative approximation is a powerful method for derivative approximations which has been successfully implemented in deterministic numerical algorithms. We explore and analyze its implementation in noisy environment through examples, error analysis and application to optimization methods. Numerical results show a promising performance of the complex-step gradient approximation in...

article

Preconditioned conjugate gradient methods for the solution of Love’s integral equation with very small parameter

Fu-Rong Lin, Yong-Jie Shi

Journal of Computational and Applied Mathematics > 2018 > 327 > Complete > 295-305

In this paper, we propose efficient numerical methods for the solution of the following Love’s integral equation f ( x ) + 1 π ∫ − 1 1 c ( x − y ) 2 + c 2 f ( y ) d y = 1 , x ∈ [ − 1 , 1 ] , where c > 0 is a very small parameter. We introduce a new unknown function h ( x ) = f ( x ) − 0 . 5 as in Lin et al. (2013), and then apply a composite...

article

Designing sound deposit insurances

Hirbod Assa, Ramin Okhrati

Journal of Computational and Applied Mathematics > 2018 > 327 > Complete > 226-242

Deposit insurances were blamed for encouraging the excessive risk taking behavior during the 2008 financial crisis. The main reason for this destructive behavior was “moral hazard risk”, usually caused by inappropriate insurance policies. While this concept is known and well-studied for ordinary insurance contracts, yet needs to be further studied for insurances on financial positions. In this paper,...

article

Block Nyström type integrator for Bratu’s equation

S.N. Jator, V. Manathunga

Journal of Computational and Applied Mathematics > 2018 > 327 > Complete > 341-349

In this paper, we use a Block Nyström Method (BNM) to obtain the numerical solution for one-dimensional Bratu’s problem. The convergence analysis of the method is discussed and it is shown that the theoretical order of the method is consistent with its numerical rate of convergence. The accuracy benefit of the BNM is demonstrated by comparing it to several other known methods given in the literature...

article

Fast search local extremum for maximal information coefficient (MIC)

Shuliang Wang, Yiping Zhao, Yue Shu, Hanning Yuan, more

Journal of Computational and Applied Mathematics > 2018 > 327 > Complete > 372-387

Maximal information coefficient (MIC) is an indicator to explore the correlation between pairwise variables in large data sets, and the accuracy of MIC has an impact on the measure of dependence for each pair. To improve the equitability in an acceptable run-time, in this paper, an intelligent MIC (iMIC) is proposed for optimizing the partition on the y-axis to approximate the MIC with good accuracy...

article

The global convergence of a modified BFGS method for nonconvex functions

Gonglin Yuan, Zhou Sheng, Bopeng Wang, Wujie Hu, more

Journal of Computational and Applied Mathematics > 2018 > 327 > Complete > 274-294

The standard BFGS method plays an important role among the quasi-Newton algorithms for constrained/un-constrained optimization problems. However, Dai (2003) constructed a counterexample to demonstrate that this method may fail for non-convex functions with inexact Wolfe line searches, and Mascarenhas (2004) showed the nonconvergence of this method and other methods in the Broyden family, even with...

article

Uniform approximation to Cauchy principal value integrals with logarithmic singularity

Takemitsu Hasegawa, Hiroshi Sugiura

Journal of Computational and Applied Mathematics > 2018 > 327 > Complete > 1-11

An approximation of Clenshaw–Curtis type is given for Cauchy principal value integrals of logarithmically singular functions I ( f ; c ) = − ∫ − 1 1 f ( x ) ( log | x − c | ) ∕ ( x − c ) d x ( c ∈ ( − 1 , 1 ) ) with a given function f . Using a polynomial p N of degree N interpolating f at the Chebyshev nodes we obtain an approximation...

article

Dynamic analysis of a planetary gear system with multiple nonlinear parameters

Ling Xiang, Nan Gao, Aijun Hu

Journal of Computational and Applied Mathematics > 2018 > 327 > Complete > 325-340

Considering time-varying meshing stiffness, comprehensive gear error and piece-wise backlash nonlinearities, a torsional nonlinear dynamic model of multistage gear of planetary gear system is established. By using Runge–Kutta numerical integration method, the dynamic responses are solved, analyzed and illustrated with the bifurcation parameters variation including excitation frequency, gear backlash...

article

Control design for output tracking of delayed Boolean control networks

Yansheng Liu, Yating Zheng, Haitao Li, Fuad E. Alsaadi, more

Journal of Computational and Applied Mathematics > 2018 > 327 > Complete > 188-195

This paper investigates the output tracking control of delayed Boolean control networks (DBCNs) by using the algebraic state space representation method. Firstly, the output tracking control problem of DBCNs is formulated, and the dynamics of DBCNs is converted into an equivalent algebraic form. Secondly, based on the algebraic form and controllability of DBCNs, a necessary and sufficient condition...

article

Barycentric interpolation collocation methods for solving linear and nonlinear high-dimensional Fredholm integral equations

Hongyan Liu, Jin Huang, Yubin Pan, Jipei Zhang

Journal of Computational and Applied Mathematics > 2018 > 327 > Complete > 141-154

In this article two barycentric interpolation collocation methods are proposed for solving linear and nonlinear high-dimensional F r e d h o l m integral equations of the second kind. The approaches respectively utilize the modified weighted L a g r a n g e functions and the novel rational functions as the interpolation basis functions. They are effective schemes for evaluating the multidimensional...

article

Existence of positive solutions for the nonlinear elastic beam equation via a mixed monotone operator

I.J. Cabrera, B. López, K. Sadarangani

Journal of Computational and Applied Mathematics > 2018 > 327 > Complete > 306-313

In this paper, we use a mixed monotone operator method to investigate the existence and uniqueness of positive solution to a nonlinear fourth-order boundary value problem which describes the deflection of an elastic beam with the left extreme fixed and the right extreme is attached to a bearing device given by a known function. Moreover, we present a concrete example illustrating the result obtained.

article

On a new class of special functions generated by integral-difference operators

Yuri B. Melnikov, Irina V. Turuntaeva

Journal of Computational and Applied Mathematics > 2018 > 327 > Complete > 167-174

We introduce and investigate a new class of special functions Ξ N [ k ] ( x ) , x ∈ [ 0 , 1 ) . Originally these functions naturally appeared upon spectral analysis of integral-difference operators. We discuss issues of generating functions; decompositions in series; links to Legendre polynomials, complete elliptic integrals and Gauss hypergeometric functions; functional relations...

article

Error analysis of a meshless weak form method based on radial point interpolation technique for Sivashinsky equation arising in the alloy solidification problem

Mohammad Ilati, Mehdi Dehghan

Journal of Computational and Applied Mathematics > 2018 > 327 > Complete > 314-324

In this paper, meshless weak form techniques are applied to find the numerical solution of nonlinear biharmonic Sivashinsky equation arising in the alloy solidification problem. Stability and convergence analysis of time-discrete scheme are proved. An error analysis of meshless global weak form method based on radial point interpolation technique is proposed for this nonlinear biharmonic equation...

article

Traub-Gander’s family for the simultaneous determination of multiple zeros of polynomials

M.S. Petković, L.D. Petković

Journal of Computational and Applied Mathematics > 2018 > 327 > Complete > 362-371

By combining Traub-Gander’s family of third order for finding a multiple zero and suitable corrective approximations od Schröder’s and Halley’s type, a new family of iterative methods for the simultaneous approximation of multiple zeros of algebraic polynomials is proposed. Taking various forms of a function involved in the iterative formula, a number of different simultaneous methods can be obtained...

article

A self-learning approach for optimal detailed scheduling of multi-product pipeline

Zhang Haoran, Liang Yongtu, Liao Qi, Shen Yun, more

Journal of Computational and Applied Mathematics > 2018 > 327 > Complete > 41-63

Pipeline transportation is cost-optimal in refined product transportation. However, the optimization of multi-product pipeline scheduling is rather complicated due to multi-batch sequent transportation and multi-point delivery. Even though many scholars have conducted researches on the issue, there is hardly a model settling the discontinuous constraints in the model as a result of batch interface...

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An equivalence lemma for a class of fuzzy implicit integro-differential equations

Numerical integration based on hyperfunction theory

A modified Lavrentiev iterative regularization method for analytic continuation

The direct method of lines for elliptic problems in star-shaped domains

An algorithm for finding intersection between ball B-spline curves

Complex-step derivative approximation in noisy environment

Preconditioned conjugate gradient methods for the solution of Love’s integral equation with very small parameter

Designing sound deposit insurances

Block Nyström type integrator for Bratu’s equation

Fast search local extremum for maximal information coefficient (MIC)

The global convergence of a modified BFGS method for nonconvex functions

Uniform approximation to Cauchy principal value integrals with logarithmic singularity

Dynamic analysis of a planetary gear system with multiple nonlinear parameters

Control design for output tracking of delayed Boolean control networks

Barycentric interpolation collocation methods for solving linear and nonlinear high-dimensional Fredholm integral equations

Existence of positive solutions for the nonlinear elastic beam equation via a mixed monotone operator

On a new class of special functions generated by integral-difference operators

Error analysis of a meshless weak form method based on radial point interpolation technique for Sivashinsky equation arising in the alloy solidification problem

Traub-Gander’s family for the simultaneous determination of multiple zeros of polynomials

A self-learning approach for optimal detailed scheduling of multi-product pipeline

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