]>
2015
14
2
95
A Fictitious Time Integration Method for a One-dimensional Hyperbolic Boundary Value Problem
A Fictitious Time Integration Method for a One-dimensional Hyperbolic Boundary Value Problem
en
en
This paper gives an estimate for the initial-boundary value problem of wave equations by using the
Fictitious Time Integration Method (FTIM) previously developed by Liu and Atluri [1]. Given examples
confirm that FTIM is highly efficient approach to find the true solutions. It is interesting that the FTIM
can easily treat the boundary value problems without any iteration and has high efficiency and high
accuracy.
87
96
Mir Sajjad
Hashemi
Maryam
Sariri
Wave Equation
method of line
Fictitious Time Integration Method
Group preserving scheme
Lie group
Geometric numerical integration.
Article.1.pdf
[
[1]
C.-S. Liu, S. N. Atluri, A novel time integration method for solving a large system of non-linear algebraic equations, CMES, 31 (2008), 71-83
##[2]
C.-S. Liu, Cone of non-linear dynamical system and group preserving schemes, Int. J. Non-Linear Mech. , 36 (2001), 1047-1068
##[3]
C.-S. Liu, Group preserving scheme for backward heat conduction problems, Int. J. Heat Mass Transfer , 47 (2004), 2567-2576
##[4]
H.-C. Lee, C.-K. Chen, C.-I. Hung, A modified group-preserving scheme for solving the initial value problems of stiff ordinary differential equations, Appl. Math. Comput. , 133 (2002), 445-459
##[5]
S. Abbasbandy, M. S. Hashemi, Group preserving scheme for the Cauchy problem of the Laplace equation, Eng. Anal. Bound. Elem. , 35 (2011), 1003-1009
##[6]
M. S. Hashemi, M. C. Nucci, S. Abbasbandy, Group analysis of the modified generalized Vakhnenko equation, Commun. Nonlinear Sci. Numer. Simulat. , 18 (2013), 867-877
##[7]
C.-S. Liu, Two-dimensional bilinear oscillator: group-preserving scheme and steady-state motion under harmonic loading, Int. J. Non-Linear Mech. , 38 (2003), 1581-1602
##[8]
C.-S. Liu, One-step GPS for the estimation of temperature-dependent thermal conductivity, Int. J. Heat Mass Transfer , 49 (2006), 3084-3093
##[9]
C.-S. Liu, A fictitious time integration method for two-dimensional quasilinear elliptic boundary value problems, CMES: Computer Modeling in Engineering & Sciences, 33 (2008), 179-198
##[10]
C.-S. Liu, A fictitious time integration method for solving the discretized inverse Sturm-Liouville problems, for specified eigenvalues, CMES: Computer Modeling in Engineering & Sciences, 36 (2008), 261-286
##[11]
C.-S. Liu, A fictitious time integration method for solving m-point boundary value problems, CMES: Computer Modeling in Engineering & Sciences, 39 (2009), 125-154
##[12]
C.-S. Liu, A fictitious time integration method for a quasilinear elliptic boundary value problem defined in an arbitrary plane domain, CMC: Computers, Materials & Continua, 11 (2009), 15-32
##[13]
C.-S. Liu, S. N. Atluri, A novel time integration method for solving a large system of non-linear algebraic equations, CMES: Computer Modeling in Engineering & Sciences, 31 (2008), 71-83
##[14]
C.-S. Liu, S. N. Atluri, A fictitious time integration method (FTIM) for solving mixed complementarity problems with applications to non-linear optimization, CMES: Computer Modeling in Engineering & Sciences, 34 (2008), 155-178
##[15]
C.-S. Liu, S. N. Atluri, A fictitious time integration method for the numerical solution of the Fredholm integral equation and for numerical differentiation of noisy data, and its relation to the filter theory, CMES: Computer Modeling in Engineering & Sciences, 41 (2009), 243-261
]
On the Existence of Multiple Solutions of a Class of Second-order Nonlinear Two-point Boundary Value Problems
On the Existence of Multiple Solutions of a Class of Second-order Nonlinear Two-point Boundary Value Problems
en
en
A general approach is presented for proving existence of multiple solutions of the second-order
nonlinear differential equation
\[u'' (x) + f (u(x)) = 0,\quad x\in [0,1], \]
subject to given boundary conditions: \(u(0) = B_1, u(1) = B_2\) or \(u'(0) = B'_1, u(1)=B_2\). The proof is
constructive in nature, and could be used for numerical generation of the solution or closed-form
analytical solution by introducing some special functions. The only restriction is about \(f(u)\) , where it is
supposed to be differentiable function with continuous derivative. It is proved the problem may admit no
solution, may admit unique solution or may admit multiple solutions.
97
107
E.
Shivanian
F.
Abdolrazaghi
Closed-form solution
exact analytical solution
special function
unique solution
multiple solutions.
Article.2.pdf
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I. Muhammed, A. Hamdan, An efficient method for solving Bratu equations, Appl. Math. Comput. , 176 (2006), 704-713
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S. Abbasbandy, E. Shivanian, Prediction of multiplicity of solutions of nonlinear boundary value problems: Novel application of homotopy analysis method, Commun. Nonlinear Sci. Numer. Simulat. , 15 (2010), 3830-3846
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S. Abbasbandy, E. Shivanian, Application of variational iteration method for nth-order integro-differential equations, Zeitschrift für Naturforschung A , 64 (2014), 439-444
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S. Abbasbandy, E. Shivanian, I. Hashim, Exact analytical solution of forced convection in a porous-saturated duct, Communications in Nonlinear Science and Numerical Simulation, 16 (10) (), 3981-3989
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E. Shivanian, S. Abbasbandy, Predictor homotopy analysis method: Two points second order boundary value problems, Nonlinear Analysis: Real World Applications , 15 (2014), 89-99
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]
Robust Trajectory Tracking for a Flexible Probe in the Presence of Uncertainties and Disturbance
Robust Trajectory Tracking for a Flexible Probe in the Presence of Uncertainties and Disturbance
en
en
This paper investigates the trajectory tracking of a bio-inspired flexible probe in medical where there exist of uncertainty and disturbance in the system. In the first approach, a sliding mode controller is designed to deal with the uncertainties and output disturbances in the system. In this case, it is assumed that the upper band of uncertainty in the system is known, but in practice this may not be really possible. Therefore, in the next section, the sliding mode controller has been extended to a robust – adaptive controller in such a way that even if there is no information on the uncertainty upper bond, the system is still stable and the probe continues to track the desired trajectory. In this case, an adaptive rule has been designed to estimate the upper bound of the uncertainty and disturbance. A numerical simulation shows the effectiveness of the proposed methodologies.
108
123
S.
Zamiri
A. Vahidian
Kamyad
Bio-inspired flexible probe
Sliding mode control
Robust-adaptive control.
Article.3.pdf
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[1]
N. Abolhassani, R. Patel, M. Moallem , Needle insertion into soft tissue, e: A survey, Medical Engineering & Physics , 29 (2007), 413-431
##[2]
B. Davies, Medical robotics a bright future, The Lancet , 368 (2006), 1-53
##[3]
G. Dogangil, B. L. Davies, F. Rodriguez Baena , A review of medical robotics for minimally invasive soft tissue surgery, Proceedings of the Institution of Mechanical, (2008)
##[4]
G. Fichtinger, T. DeWeese, A. Patriciu et. al., System for robotically assisted prostate biopsy and therapy with intraoperative CT guidance, Acad Radiol, 9(1) (2004), 60-74
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R. Alterovitz, J. Pouliot, R. Taschereau, I. Hsu, K. Goldberg, Simulating needle insertion and radioactive seed implantation for prostate brachytherapy, Stud. in Health Tech. and Informat., (2003), 19-25
##[6]
N. Abolhassani, R. Patel, M. Moallem, Needle insertion into soft tissue: A survey, Med. Eng. and Phys., 29(4) (2009), 413-431
##[7]
R. Webster, J. Kim, N. Cowan, G. Chirikjian, A. Okamura, Nonholonomic modeling of needle steering, The Intl. J. of Rob. Res, 25(5-6) (2006), 1-509
##[8]
S. Misra, K. Reed, A. Douglas, K. Ramesh, A. Okamura, Needletissue interaction forces for bevel-tip steerable needles, in Proc. IEEE Int. Conf. on Biomed. Rob. and Biomechat., (2008), 224-231
##[9]
S. P. DiMaio, S. E. Salcudean, Needle insertion modeling and simulation, IEEE Trans. on Rob. and Auto., 19(5) (2005), 864-875
##[10]
C. Duriez, C. Guébert, M. Marchal, S. Cotin, L. Grisoni, Interactive simulation of flexible needle insertions based on constraint models, in Proc. of MICCAI, (2009), 291-299
##[11]
R. Alterovitz, K. Goldberg, A. Okamura, Planning for steerable bevel-tip needle insertion through 2d soft tissue with obstacles, in Proc. of ICRA, (2007), 1640-1645
##[12]
S. P. DiMaio, S. E. Salcudean, Needle steering and model-based trajectory planning, MICCAI, (2006), 33-40
##[13]
V. Duindam, R. Alterovitz, S. Sastry, K. Goldberg, Screw-based motion planning for bevel-tip flexible needles in 3d environments with obstacles, ICRA, (2009), 2483-2488
##[14]
D. Glozman, M. Shoham, Flexible needle steering and optimal trajectory planning for percutaneous therapies, MICCAI, (2004), 137-144
##[15]
L. Frasson, S. Y. Ko, A. Turner, T. Parittotokkaporn, J. F. Vincent, F. Rodriguez y Baena, STING, A soft-tissue intervention and neurosurgical guide to access deep brain lesions through curved trajectories, Proceedings of the Institution of Mechanical Engineers-Part H: Journal of Engineering in Medicine , 224 (2010), 775-788
##[16]
S. Y. Ko, L. Frasson, B. L. Davies, F. Rodriguez y Baena , Software and hardware integration of a biomimetic flexible probe within the ROBOCAST neurosurgical robotic suite, Hamlyn Symposium on Medical Robotics, London, UK (2010)
##[17]
G. Fichtinger, T. DeWeese, A. Patriciu et. al., System forrobotically assisted prostate biopsy and therapy with intraoperativeCT guidance, Acad Radiol, 9(1) (2002), 60-74
##[18]
N. Abolhassani, R. Patel, M. Moallem, Needle insertion into softtissue: A survey, Med. Eng. and Phys., 9(4) (2007), 413-431
##[19]
D. Glozman, M. Shoham, Flexible needle steering and optimal trajectory planning for percutaneous therapies, in Proc. of MICCAI, (2004), 137-144
##[20]
N. Abolhassani, R. Patel, F. Ayazi, Minimization of needle deflection in robot-assisted percutaneous therapy, Int. J. of Med.Robot. and Comp. Assis. Surg., 3(2) (2007), 140-148
##[21]
S. Misra, K. Reed, A. Douglas, K. Ramesh, A. Okamura, Needletissue interaction forces for bevel-tip steerable needles, in Proc. IEEE Int. Conf. on Biomed. Rob. and Biomechat., (2008), 224-231
##[22]
S. P. DiMaio, S. E. Salcudean, Needle insertion modeling and simulation, IEEE Trans. on Rob. and Auto., 19(5) (2003), 864-875
##[23]
C. Duriez, C. Guebert, M. Marchal, S. Cotin, L. Grisoni, Interactive simulation of flexible needle insertions based on constraintmodels, in Proc. of MICCAI, (2009), 291-299
##[24]
R. Alterovitz, K. Goldberg, A. Okamura, Planning for steerable bevel-tip needle insertion through 2d soft tissue with obstacles, inProc. of ICRA, (2005), 1640-1645
##[25]
S. P. DiMaio, S. E. Salcudean, Needle steering and model-based trajectory planning, in Proc. of MICCAI, (2003), 33-40
##[26]
V. Duindam, R. Alterovitz, S. Sastry, K. Goldberg, Screw-based motion planning for bevel-tip flexible needles in 3d environments with obstacles, Proc. of ICRA, (2008), 2483-2488
##[27]
S. Y. Ko, B. L. Davies, F. Rodriguez y Baena, Two-dimensional needle steering with a ‘‘programmable bevel’’ inspired by nature: modeling preliminaries, IEEE/RSJ International Conference on Intelligent Robots and Systems Taipei, Taiwan, (2010), 2319-2324
##[28]
S. Y. Ko, L. Frasson, F. Rodriguez y Baena, Closed-loop planar motion control of a steerable probe with a ‘‘programmable bevel’’ inspired by nature, IEEE Transactions on Robotics, 27 (2011), 970-983
##[29]
R. J. Webster, J. S. Kim, N. J. Cowan, G. S. Chirikjian, A. M. Okamura , Nonholonomic Modeling of Needle Steering, The International Journal of Robotics Research, 25 (2007), 509-525
##[30]
R. Alterovitz, M. Branicky, K. Goldberg , Motion Planning Under Uncertainty for Image-guided Medical Needle Steering, The International Journal of Robotics Research, 27 (2009), 1361-1374
##[31]
T. R. Wedlick, A. M. Okamura, Characterization of pre-curved needles for steering in tissue, in Proc. Annu. Int. Conf. IEEE Eng. Med. Biol.Soc., Sep., (2009), 1200-1203
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P. J. Swaney, J. Burgner, H. B. Gilbert, R. J. Webster, A flexure based steerable needle: High curvature with reduced tissue damage, IEEE Trans. Biomed. Eng., 60(4) (2013), 906-909
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S. Okazawa, R. Ebrahimi, J. Chuang, S. E. Salcudean, R. Rohling, Hand-held steerable needle device, IEEE/ASME Trans. Mechatronics, 10(3) (2005), 285-296
##[34]
S. Y. Ko, L. Frasson, F. R. y Baena, Closed-loop planar motion control of a steerable probe with a programmable bevel inspired by nature, IEEE Trans. Robot., 27(5) (2011), 970-983
##[35]
K. B. Reed, A. M. Okamura, N. J. Cowan , Modeling and Control of Needles with Torsional Friction, IEEE Transactions on Biomedical Engineering, 56 (2009), 2905-2916
##[36]
D. Glozman, M. Shoham , Flexible Needle Steering and Optimal Trajectory Planning for Percutaneous Therapies, Lecture Notes in Computer Science, 3217 (2005), 137-144
##[37]
D. Glozman, M. Shoham, Image-Guided Robotic Flexible Needle Steering, IEEE transactions on robotics, 23 (2008), 459-467
##[38]
S. Young Ko, F. Rodriguez y Baena, Trajectory following for a flexible probe with state/input constraints: An approach based on model predictive control, Robotics and Autonomous Systems, 60 (2012), 509-521
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D. S. Minhas, J. A. Engh, M. M. Fenske, C. N. Riviere, Modeling of Needle Steering via Duty-Cycled Spinning, in the 29th Annual International Conference of the IEEE EMBS, Lyon, France, (2007), 2756-2759
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D. Minhas, J. A. Engh, C. N. Riviere, Testing of Neurosurgical Needle Steering via Duty-Cycled Spinning in Brain Tissue in Vitro, in IEEE EMBS, Minneapolis, Minnesota, USA, (2009), 258-261
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N. A. Wood, K. Shahrour, M. C. Ost, C. N. Riviere , Needle Steering System using Duty-Cycled Rotation for Percutaneous Kidney Access, in International Conference of the IEEE EMBS, Buenos Aires, Argentina, (2010), 5432-5435
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D. Glozman, M. Shoham , Image-Guided Robotic Flexible Needle Steering, IEEE Transactions on Robotics, 23 (2007), 459-467
]
Rational Laguerre Functions and Their Applications
Rational Laguerre Functions and Their Applications
en
en
In this work, we introduce a new class of rational basis functions defined on \([a,b)\) and based on mapping
the Laguerre polynomials on the bounded domain \([a,b)\) . By using these rational functions as basic
functions, we implement spectral methods for numerical solutions of operator equations. Also the
quadrature formulae and operational matrices (derivative, integral and product) with respect to these basis
functions are obtained. We show that using quadrature formulae based on rational Laguerre functions give
us very good results for numerical integration of rational functions and also implementing spectral methods
based on these basis functions for solving stiff systems of ordinary differential equationsgive us suitable
results. The details of the convergence rates of these basis functions for the solutions of operator equations
are carried out, both theoretically and computationally and the error analysis is presented in \(L^2 [a,b)\)
space norm.
124
142
A.
Aminataei
S. Ahmadi
Asl
Z.
Kalatehbojdi
Rational Laguerre functions
Spectral methods
Quadrature formulae
Stiff system
Hilbert space.
Article.4.pdf
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[1]
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]
Drug Administered Cancer Model Under One Term Delay
Drug Administered Cancer Model Under One Term Delay
en
en
A mathematical model is presented here that describes the growth of tumor cells and intrinsic behavior of it in the presence of immune cells. In this model we have also considered another drug variable which has the effect on both the cells. Hence it is a model for cancer that contains immune, tumor and drug. The model is highly nonlinear in nature. The effect of growth of normal cell is not considered. Constant number of immune cells is assumed to be present in the system. In this model we have considered a delay term in the growth of tumor which makes the model more realistic. We also assume that drug kills both immune cells and tumor cells simultaneously in different rate. Stability of both immune and tumor cells with and without delay has been analyzed under equilibrium condition analytically as well as numerically. It is found that the stability of the model depends on both tumor cells as well as on the delay.
143
150
Aditya
Ghosh
Anuradha
Devi
Mathematical model
Tumor cell
Immune cell
Drug
Stability
Delay
Article.5.pdf
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[1]
J. A. Adam , The dynamics growth-factor-modified immune response to cancer growth:One- dimensional models, Mathematical andComputer modelling , 17 (1993), 83-106
##[2]
J. A. Adam , J. Panetta, A simple mathematical model and alternative paradigmfor certain chemotherapeutic regimens, Mathematical and Computer modelling , 22 (8) (1995), 49-60
##[3]
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Restarted State Parameterization Method for Optimal Control Problems
Restarted State Parameterization Method for Optimal Control Problems
en
en
In this paper we introduce an efficient algorithm based on state parameterization method to solve optimal control problems and Van Der Pol oscillator. In fact, state variable can be considered as linear combination of polynomials with unknown coefficients. Using this method, an optimal control problem breaks down into an optimization and will be solved via mathematical programming techniques. By this algorithm, the control and state variables can be approximated as a function of time. Finally, some numerical examples are presented to show the validity and efficiency of the proposed method.
151
161
B.
Kafash
A.
Delavarkhalafi
Optimal control problems
State parameterization method
Mathematical programming techniques
Van Der Pol oscillator.
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Modification of the Hpm by Using Optimal Newton Interpolation Polynomial for Quadratic Riccati Differential Equation
Modification of the Hpm by Using Optimal Newton Interpolation Polynomial for Quadratic Riccati Differential Equation
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en
In this work, an efficient modification of the homotopy analysis method by using optimal Newton interpolation polynomials is given for the approximate solutions of the Riccati differential equations. This presented method can be applied to linear and nonlinear models. Examples show that the method is effective.
162
170
F.
Ghomanjani
F.
Divandar
quadratic Riccati differential equation
modification of the HPM
Newton interpolation.
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]
A New Fuzzy Membership Assignment Approach for Fuzzy Svm Based on Adaptive Pso in Classification Problems
A New Fuzzy Membership Assignment Approach for Fuzzy Svm Based on Adaptive Pso in Classification Problems
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en
Noises will confuse Support Vector Machine (SVM) in the training phase. To overcome this problem, SVM was extended to Fuzzy SVM (FSVM) by incorporating an appropriate fuzzy membership to each data point. Thus, how to choose a proper fuzzy membership is of paramount importance in FSVM. In this paper, Adaptive Particle Swarm Optimization (APSO) method minimizes the generalization error by changing the attributes values of positive and negative class centers to make them free of attribute-noise. As the APSO converged, the fuzzy memberships are assigned for each training data points based on their distance to the corresponding purified class centers with the same class-label. To demonstrate the effectiveness of the proposed FSVM, its performance on artificial and real-world data sets is compared with three FSVM algorithms in the literature.
171
182
Omid Naghash
Almasi
Hamed Sadeghi
Gooqeri
Behnam Soleimanian
Asl
Wan Mei
Tang
Fuzzy support vector machine
Fuzzy membership function
Adaptive particle swarm optimization
Attribute-noise.
Article.8.pdf
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