• Journal of applied mathematics & informatics
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• v.35 no.1_2
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• pp.165-180
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• 2017

In this study, Taylor matrix algorithm is designed for the approximate solution of linear and non-linear differential equation systems. The algorithm is essentially based on the expansion of the functions in differential equation systems to Taylor series and substituting the matrix forms of these expansions into the given equation systems. Using the Mathematica program, the matrix equations are solved and the unknown Taylor coefficients are found approximately. The presented numerical approach is discussed on samples from various linear and non-linear differential equation systems as well as stiff systems. The computational data are then compared with those of some earlier numerical or exact results. As a result, this comparison demonstrates that the proposed method is accurate and reliable.

• Kyungpook Mathematical Journal
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• v.61 no.2
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• pp.383-393
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• 2021

In this paper, numerical techniques are presented for solving initial value problems of fractional differential equations with variable coefficients. The method is derived by applying a Taylor vector approximation. Moreover, the operational matrix of fractional integration of a Taylor vector is provided in order to transform the continuous equations into a system of algebraic equations. Furthermore, numerical examples demonstrate that this method is applicable and accurate.

• Journal of applied mathematics & informatics
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• v.32 no.5_6
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• pp.747-760
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• 2014

In this paper a higher order iterative algorithm is developed for an unconstrained multivariate optimization problem. Taylor expansion of matrix valued function is used to prove the cubic order convergence of the proposed algorithm. The methodology is supported with numerical and graphical illustration.

• The Journal of the Korea Contents Association
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• v.11 no.1
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• pp.404-410
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• 2011

For the simulation of one-dimensional unsteady flow, the Taylor-Galerkin finite element method was adopted to the discretization of the Saint Venant equation. The model was applied to the backwater problem in a single channel and the flood routing in dendritic channel networks. The numerical solutions were compared with previously published results of finite difference and finite element methods and good agreement was observed. The model solves the continuity and the momentum equations in a sequential manner and this leads to easy implementation. Since the final system of matrix is tri-diagonal with a few additional entry due to channel junctions, the tri-diagonal matrix solution algorithm can be used with minor modification. So it is fast and economical in terms of memory for storing matrices.

• Honam Mathematical Journal
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• v.44 no.3
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• pp.310-324
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• 2022

In this paper, we define timelike curves in R⁴₂ and characterize such curves in terms of Frenet frame. Also, we examine the timelike helices of R⁴₂, taking into account their curvatures. In addition, we study timelike slant helices, timelike B₁-slant helices, timelike B₂-slant helices in four dimensional semi-Euclidean space, R⁴₂. And then we obtain an approximate solution for the timelike B₁ slant helix with Taylor matrix collocation method.

• Journal of Korean Society of Steel Construction
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• v.26 no.3
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• pp.143-154
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• 2014

An improved method for evaluating effective buckling length of semi-rigid frame with inelastic behavior is newly proposed. Also, generalized exact tangential stiffness matrix with rotationally semi-rigid connections is adopted in previous studies. Therefore, the system buckling load of structure with inelastic behaviors can be exactly obtained by only one element per one straight member for inelastic problems. And the linearized elastic stiffness matrix and the geometric stiffness matrix of semi-rigid frame are utilized by taking into account 4th terms of taylor series from the exact tangent stiffness matrix. On the other hands, two inelastic analysis programs(M1, M2) are newly formulated. Where, M1 based on exact tangent stiffness matrix is programmed by iterative determinant search method and M2 is using linear algorithm with elastic and geometric matrices. Finally, in order to verify this present theory, various numerical examples are introduced and the effective buckling length of semi-rigid frames with inelastic materials are investigated.

• Journal of Mechanical Science and Technology
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• v.15 no.7
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• pp.847-858
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• 2001

This paper considers the control model identification and H(sub)$\infty$ controller design for a tandem cold mill (TCM). In order to improve the performance of the existing automatic gauge control (AGC) system based on the Taylor linearized model of the TCM, a new mathematical model that can complement the Taylor linearized model is constructed by using the N4SID algorithm based on subspace method and the least squares algorithm based on ARX model. It is shown that the identified model had dynamic characteristics of the TCM than the existing Taylor linearized model. The H(sub)$\infty$ controller is designed to have robust stability to the system parameters variation, disturbance attenuation and robust tracking capability to the set-up value of strip thickness. The H(sub)$\infty$ servo problem is formulated and it is solved by using LMI (linear matrix inequality) techniques. Simulation results demonstrate the usefulness and applicability of the proposed H(sub)$\infty$ controller.

• Journal of Satellite, Information and Communications
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• v.10 no.1
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• pp.22-28
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• 2015

In this paper, we propose a new computationally efficient joint iterative multi-input multi-output (MIMO) detection scheme using a soft interference cancellation and minimum mean squared-error (SIC-MMSE) method. The critical computational burden of the SIC-MMSE scheme lies in the multiple inverse operations of the complex matrices. We find a new way which requires only a single matrix inversion by utilizing the Taylor series expansion of the matrix, and thus the computational complexity can be reduced. The computational complexity reduction increases as the number of antennas is increased. The simulation results show that our method produces almost the same performances as the conventional SIC-MMSE with reduced computational complexity.

• Transactions of the Korean Society of Mechanical Engineers
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• v.9 no.1
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• pp.31-39
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• 1985

Using the tensor elastic Green functions an exact integral equation is formulated for two anisotropic precipitates embedded in an infinite anisotropic matrix; the matrix is subjected to an applied strain field or the precipitates undergo a stress-free transformation strain. This equation is reduced to an infinite system of algebraic equations by expanding the strains in Taylor series about the two points within each precipitate, and an approximation of the strain distributions within the two spherical precipitates is obtained by truncating the higher order terms. Since the present method requires no symmetry conditio between the two shperical precipitates, it is possible to obtain the strain distribution within the precipitates when the elastic constants and/or the sizes of the precipitates are different each other. The strains are expanded about arbitrary points, giving more accurate distributions of the strains than those presented elsewhere. The present method can be directly estended to the case of more than two spherical precipitates.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.33 no.2
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• pp.409-422
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• 2013

For stability design and P-${\Delta}$ analysis of steel frames with semi-rigid connections, the explicit form of the exact tangential stiffness matrix of a generalized semi-rigid frame element having rotational and translational connections is firstly derived using the stability functions. And its elastic and geometric stiffness matrix is consistently obtained by Taylor series expansion. Next depending on connection types of semi-rigidity, the corresponding tangential stiffness matrices are degenerated based on penalty method and static condensation technique. And then numerical procedures for determination of effective buckling lengths of generalized semi-rigid frames members and P-${\Delta}$ and shortly addressed. Finally three numerical examples are presented to demonstrate the validity and accuracy of the proposed method. Particularly the minimum braced frames and coupled buckling modes of the corresponding frames are investigated.