Tzyy-Leng Horng

Distinguished Professor

Ph.D., Engineering, Brown University, U.S.A.

Research areas

Numerical methods for PDEs, Computational fluid dynamics and heat transfer, Mathematical modeling and computer simulation for biology and physiology


Calculus, Numerical Methods and Analysis, Applied Mathematic, Hyperbolic PDEs, Ordinary Differential Equations, Mathematical Biology

  • Profile
  • Publications
  • Research & Teaching


  • Ph.D., Engineering, Brown University (May 1992)
  • M.S., Applied Mathematics, Brown University (May 1992)
  • M.S., Aerospace and Mechanical Engineering, University of Arizona (May 1988)
  • B.S., Mechanical Engineering, National Taiwan University (June 1983)



  • Distinguished Professor, Feng Chia University, Aug. 2015-present.
  • Professor, Department of Applied Mathematics, Feng Chia University, Aug. 2007-present.
  • Associate Professor, Department of Applied Mathematics, Feng Chia University, Feb. 1993-Jul. 2007.
  • Professor, Ph. D. program of Mechanical and Aeronautical Engineering, Feng Chia University , Aug. 2007-present.
  • Associate Professor, Ph. D. program of Mechanical and Aeronautical Engineering, Aug. 2002-Jul. 2007.
  • Professor, Bachelor's Program of Financial Engineering and Actuarial Science, Feng Chia University , Feb. 2013-present.
  • Visiting Professor, Rush University Medical Center , June 2011-Aug. 2011.
  • Post-doctoral research associate, Brown University, May 1992-Oct. 1992.
  • Research assistant, Brown University, Sep. 1988-May 1992.
  • Teaching assistant, Brown University, Sep. 1991-May 1992.
  • Research assistant, University of Arizona, Aug. 1985-May 1988.

Recent Refereed Papers

  • Tzu-Ching Shih*, Hao-Li Liu, and Tzyy-Leng Horng, 2006, "Cooling effect of thermally significant blood vessels in perfused tumor tissue during thermal therapy," International Communications in Heat and Mass Transfer, 33:135-141 (reprint). (SCI,  impact factor 2.782, rank MECHANICS 9/137, cited by 25)
  • Jerry M. Chen*, Tzyy-Leng Horng, and Wei Yee Tan, 2006, "Analysis and measurements of mixing in pressure-driven microchannel flow," Microfluidics and Nanofluidics, 2(6):455-469 (reprint). (SCI, impact factor  2.528, rank INSTRUMENT & INSTRUMENTATION 7/56, cited by 36)
  • Chu-Pin Lo, Tzyy-Leng Horng*, Hsiang-Ning Luk, Hui-Chun Tien, Juan-Ming Yuan, and Daniel Lee, 2006, "A computational model of the canine pulmonary veins sleeves," Journal of Medical and Biological Engineering, 26(3):125-130 (reprint). (SCI, impact factor 0.971, rank ENGINEERING, BIOMEDICAL 62/76, cited by 1)
  • Tzyy-Leng Horng* and Ming-Wai Huang, 2006, "Spontaneous oscillations in Hodgkin-Huxley model," Journal of Medical and Biological Engineering, 26(4):161-168 (reprint). (SCI, impact factor 0.971, rank ENGINEERING, BIOMEDICAL 62/76 , cited by 1)
  • T.-L. Horng, S.-C. Gou*, and T.-C. Lin, 2006, "Bending-wave instability of a vortex ring in a trapped Bose-Einstein condensate," Physical Review A, Rapid Communications, 74:041603(R) (reprint). (SCI, impact factor 2.808, rank OPTICS 16/87, cited by 23)
  • Tzyy-Leng Horng, Win-Li Lin, Ching-Tsung Liauh, and Tzu-Ching Shih*, 2007, "Effects of pulsatile blood flow in large vessels on thermal dose distribution during thermal therapy," Medical Physics, 34(4):1312-1320 (reprint). (SCI  impact factor 2.635, rank RADIOLOGY, NUCLEAR MEDICINE & MEDICAL IMAGING 38/125, cited by 36)
  • Tzyy-Leng Horng* and Chih-Yuan Tien, 2006, "American options valuation: A parsimoniously numerical approach," (preprint). (cited by 1)
  • C.-H. Hsueh, S.-C. Gou*, T.-L. Horng, and Y.-M. Kao, 2007, "Vortex-ring solutions of Gross-Pitaevskii equation for an axisymmtrically trapped Bose-Einstein condensate," Journal of Physics B: Atomic, Molecular & Optical Physics, 40:1-11 (reprint). (SCI impact factor 1.975, rank OPTICS 28/87, cited by 13)
  • T.-L. Horng, C.-H. Hsueh, and S.-C. Gou*, 2008, "Transition to Quantum Turbulence in Bose-Einstein Condensate through Bending-wave Instability of a Single Vortex Ring ," Physical Review A, 77:063625,(reprint)(supplemental animation 1)(supplemental animation 2)(supplemental animation 3),(supplemental animation 4)(supplemental animation 5)(supplemental animation 6). (SCI, impact factor 2.808, rank OPTICS 16/87, cited by 26)
  • Yu-Cheng Hsieh, Tzyy-Leng Horng, Shien-Fong Lin, Tung-Chao Lin, Chih-Tai Ting, and Tsu-Juey Wu*, 2009, "D,l-Sotalol at therapeutic concentrations facilitates the occurrence of long-lasting non-stationary reentry during ventricular fibrillation in isolated rabbit hearts," Circulation Journal, 73(1):39-47 (reprint). (SCI,  impact factor 3.940, rank CARDIAC & CARDIOVASCULAR SYSTEMS 30/123 , cited by 7)
  • Dedy Zulhidayat Noor*, Ming-Jyh Chern, Tzyy-Leng Horng, 2009, "An immersed boundary method to solve fluid–solid interaction problems," Computational Mechanics, 44(4):447-454 (reprint). (SCI , impact factor 2.525, rank MATHEMATICS, INTERDISCIPLINARY APPLICATIONS 8/99, cited by 23)
  • T.-L. Horng, S.-C. Gou, T.-C. Lin, G.A. El, A.P. Itin, and A.M. Kamchatnov*, 2009, "Stationary wave patterns generated by an impurity moving with supersonic velocity through a Bose-Einstein condensate," Physical Review A, 79:053619 (reprint). (SCI, impact factor 2.808, rank OPTICS 16/87, cited by 9)
  • T.-L. Horng, C.-H. Hsueh, S.-W. Su, Y.-M. Kao, and S.-C. Gou*, 2009, "Two-dimensional quantum turbulence in a nonuniform Bose-Einstein condensate," Physical Review A, 80:023618 (reprint),(supplemental animation 1)(supplemental animation 2). (SCI, impact factor 2.808, rank OPTICS 16/87, cited by 32)
  • Huang-Wen Huang*, Tzu-Ching Shih, Chihng-Tsung Liauh and Tzyy-Leng Horng, 2009, "Computer simulation of 3-D temperature and power distributions in tissue with a countercurrent blood vessels network during hyperthermia," Journal of Medical and Biological Engineering, 29(5):252-258 (reprint). (SCI, impact factor 0.971, rank ENGINEERING, BIOMEDICAL 62/76, cited by 5)
  • Huang-Wen Huang, Chihng-Tsung Liauh, Tzu-Ching Shih, Tzyy-Leng Horng and Win-Li Lin*, 2010, "Significance of blood vessels in optimization of absorbed power and temperature distributions during hyperthermia," International Journal of Heat and Mass Transfer, 53:5651-5662 (reprint). (SCI, impact factor 2.383, rank ENGINEERING, MECHANICAL 11/139, cited by 16)
  • Shih-Wei Su, Yi-Hsin Chen, Shih-Chuan Gou*, Tzyy-Leng Horng, and Ite A. Yu, 2011, "Dynamics of slow light and light storage in a Doppler-broadened electromagnetically induced transparency medium: A numerical approach," Physical Review A, 83:013827 (reprint). (SCI, impact factor 2.808, rank OPTICS 16/87, cited by 14)
  • C.-H. Hsueh ,T.-L. Horng, S.-C. Gou, and W. C. Wu*, 2011, "Equilibrium vortex formation in ultrarapidly rotating two-component Bose-Einstein condensates," Physical Review A, 84:023610 (reprint). (SCI,  impact factor 2.808, rank OPTICS 16/87, cited by 12)
  • S.-W. Su , C.-H. Hsueh, T.-L. Horng, Y.-C. Tsai, W. M. Liu, I.-K. Liu and S.-C. Gou*, 2011, "Spontaneous crystallization of skyrmions and fractional vortices in fast-rotating and rapidly quenched spin-1 Bose-Einstein condensates," Physical Review A, 84:023601 (reprint). (SCI, impact factor 2.808, rank OPTICS 16/87, cited by 22)
  • Tzyy-Leng Horng and Chun-Hao Teng*, 2012, "An error minimized pseudospectral penalty direct Poisson solver," Journal of Computational Physics, 231(6):2498–2509 (reprint, slidematlab code #1matlab code #2). (SCI,  impact factor 2.434, rank PHYSICS, MATHEMATICAL 3/54, cited by 5)
  • Tzu-Ching Shih*, Tzyy-Leng Horng*, Huang-Wen Huang, Kuen-Cheng Ju, Tzung-Chi Huang, Po-Yuan Chen, Yung-Jen Ho and Win-Li Lin, 2012, "Numerical analysis of coupled effects of pulsatile blood flow and thermal relaxation time during thermal therapy," International Journal of Heat and Mass Transfer, 55:3763-3773 (reprint). (SCI,  impact factor 2.383, rank ENGINEERING, MECHANICAL 11/130, cited by 17)
  • C.-H. Hsueh, T.-C. Lin, T.-L. Horng, and W. C. Wu*, 2012, "Quantum crystals in a trapped Rydberg-dressed Bose-Einstein condensate," Physical Review A, 84:023601 (reprint). (SCI,  impact factor 2.808, rank OPTICS 16/87, cited by 9)
  • M.-J. Chern*, W.-C. Hsu and T.-L. Horng, 2012, "Numerical prediction of hydrodynamic loading on circular cylinder array in oscillatory flow using direct-forcing immersed boundary method," Journal of Applied Mathematics, Article ID 505916 (accepted 20 July 2012) (reprint). (SCI, impact factor 0.812, rank MATHEMATICS, APPLIED 135/257, cited by 4)
  • A. M. Kamchatnov*, Y.-H. Kuo, T.-C. Lin, T.-L. Horng, S.-C. Gou, R. Clift, G. A. El, and R. H. J. Grimshaw, 2012, "Undular bore theory for the Gardner equation," Physical Review E, 86: 036605 (reprint). (SCI, impact factor 2.288, rank PHYSICS, MATHEMATICAL 5/54, cited by 22)
  • T.-L. Horng, T.-C. Lin, C. Liu and B. Eisenberg*, 2012, "PNP equations with steric effects: a model of ion flow through channels", Journal of Physical Chemistry B, 116: 11422-11441 (reprint). (SCI, impact factor 3.302, rank CHEMISTRY, PHYSICAL 44/139, cited by 53)
  • S.H. Hsieh, G.J. Lee, C.Y. Chen, J.H. Chen, S.H. Ma, T.L. Horng, K.H. Chen, and J.J. Wu*, 2012, "Synthesis of Pt doped Bi2O3/RuO2 photocatalysts for hydrogen production from water splitting using visible light", Journal of Nanoscience and Nanotechnology, 12(7):5930-5936, (reprint). (SCI, impact factor 1.556, rank CHEMISTRY, MULTIDISCIPLINARY 74/157, cited by 5)
  • H.-W. Huang, C.-T. Liauh, T.-L. Horng, T.-C. Shih, C.-F. Chiang, W.-L. Lin*, 2013, "Effective heating for tumors with thermally significant blood vessels during hyperthermia treatment", Applied Thermal Engineering, 50:837-847, (reprint). (SCI, impact factor 2.739, rank MECHANICS 10/137, cited by 6)
  • Teng-Yao Kuo, Hsin-Chu Chen, Tzyy-Leng Horng*, 2013, "A fast poisson solver by Chebyshev pseudospectral method using reflexive decomposition," Taiwanese Journal of Mathematics, 17(4):1167–1181, (reprint). (SCI, impact factor 0.621, rank MATHEMATICS 152/312, cited by 2)
  • C.-Y. Chou, C.-K. Huang, K.-W. Lu, T.-L. Horng*, W.-L. Lin*, April 2013, "Investigation of the spatiotemporal responses of nanoparticles in tumor tissues with a small-scale mathematical model", PLoS One, 8(4):e59135, (reprint), (Supporting Information). (SCI,  impact factor 3.234, rank MULTIDISCIPLINARY SCIENCES 9/57, cited by 2)
  • M.-J. Chern*, W.-C. Shiu, and T.-L. Horng, 2013, "Immersed boundary modeling for interaction of oscillatory flow with cylinder array under effects of flow direction and cylinder arrangement," Journal of Fluids and Structures, 43:325-346, (reprint). (SCI, impact factor 2.201, rank ENGINEERING, MECHANICAL 20/130, cited by 4)
  • G. El, A. Kamchatnov*, Y.-H. Kuo, T.-C. Lin, T.-L. Horng, S.-C. Gou, R. Clift, and R. Grimshaw, 2013, "Transcritical flow of a stratified fluid over topography: analysis of the forced Gardner equation," Journal of Fluid Mechanics, 736:495-531, (reprint). (SCI , impact factor 2.383, rank MECHANICS 15/137, cited by 4)
  • Y.-C Chu, G.-J Lee, C.-Y. Chen, S.-H Ma, J Wu, T.-L Horng, K.-H Chen and J.-H Chen* , 2013, "Preparation of bismuth oxide photocatalyst and its application in white-light LEDs," Journal of Nanomaterials, Article ID 596324 (accepted 14 September 2013) (reprint). (SCI, impact factor 1.644, rank MATERIALS SCIENCE, MULTIDISCIPLINARY 122/260, cited by 4)
  • Shu-Han Hsieh, Gang-Juan Lee, Chin-Yi Chen, Jing-Heng Chen, Shih-Hsin Ma, Tzyy-Leng Horng, Kun-Huang Chen, and Jerry J. Wu*, 2013, "Hydrothermal Synthesis of Mesoporous Bi2O3/Co3O4 Microsphere and Photocatalytic Degradation of Orange II Dyes by Visible Light", Topics in Catalysis, 56(9-10):623-629 (available on line in 12 April 2013) (reprint). (SCI,impact factor 2.365, rank Chemistry, Applied 16/72, cited by 6)
  • Tzu-Ching Shih*, Huang-Wen Huang, Wei-CheWei, Tzyy-Leng Horng, 2014,"Parametric analysis of effective tissue thermal conductivity, thermal wave characteristic, and pulsatile blood flow on temperature distribution during thermal therapy," International Communications in Heat and Mass Transfer, 52:113-120 (March 2014) (reprint). (SCI,  impact factor 2.782, rank MECHANICS 9/137, cited by 3)
  • Fong-Lin Chen, Tzyy-Leng Horng and Tzu-Ching Shih*,2014, "Simulation analysis of airflow alteration in the trachea following the vascular ring surgery based on CT images using the computational fluid dynamics method," Journal of X-Ray Science and Technology, 22:213–225 (April, 2014; accepted 16 December 2013) (reprint). (SCI,  impact factor 1.398, rank OPTICS 48/87, cited by 4)
  • C. S. Lin, T. L. Horng*, J. H. Chen, K. H. Chen, J. J. Wu, C. Y. Chen, and S. H. Ma, 2014, "Mechanical Properties Measurement of Polymer Films by Bulge Test and Fringe Projection," Advances in Materials Science and Engineering, Article ID 170279 (accepted 21 April 2014, published 20 May 2014) (reprint). (SCI, impact factor 0.744, rank MATERIALS SCIENCE, MULTIDISCIPLINARY 210/260, citede by 2)
  • M. J. Chern*, Y. H. Kuan, G. Nugroho, G. T. Lu, and T. L. Horng, 2014, "Direct-forcing immersed boundary modeling of vortex-induced vibration of a circular cylinder," Journal of Wind Engineering and Industrial Aerodynamics, 134:109-121 (accepted 27 August 2014, published November 2014), (reprint). (SCI, impact factor 1.414, rank ENGINEERING, CIVIL 35/125, cited by 4)
  • A. Manivel, G.J. Lee, C.Y. Chen, J.H. Chen, S.H. Ma, T.L. Horng, and J.J. Wu*, 2015, "Synthesis of MoO3 Nanoparticles for Azo Dye Degradation by Catalytic Ozonation," Materials Research Bulletin , 62:184-191 (accepted 4 November 2014, published Feburary 2015), (reprint). (SCI, impact factor 2.288, rnak MATERIALS SCIENCE, MULTIDISCIPLINARY 67/260, cited by 7)
  • C.Y. Chen*, J.C. Weng, J.-H. Chen, S.H. Ma, K.H. Chen, T.L. Horng, C.Y. Tsay, C.J. Chang, C.K. Lin, and J.J. Wu, 2015, "Photocatalyst ZnO-Doped Bi2O3 Powder Prepared by Spray Pyrolysis," Powder Technology, 272:316-321 (accepted December 2014, published March 2015), (reprint). (SCI, impact factor 2.349, rnak ENGINEERING, CHEMICAL 39/135, cited by 4)
  • Ming-Jyh Chern, Dedy Zulhidayat Noor, Ching-Biao Liao and Tzyy-Leng Horng*, 2015, "Direct-Forcing Immersed Boundary Method for Mixed Heat Transfer," Communications in Computational Physics, 18(4):1072-1094 (accepted May 2015, published October 2015), (reprint). (SCI, impact factor 1.943, rank PHYSICS, MATHEMATICAL 10/54)   
  • Ming-Jyh Chern*, Farida Rahmawati Purnadiana, Dedy Zulhidayat Noor,Tzyy-Leng Horng, Shiu-Wu Chau, Ernest Odhiambo, 2015, "Numerical study of flow past two counter rotating cylinders using immersed boundary method," Journal of Marine Science and Technology, 23(5):761-773, (accepted June 2015, published November 2015), (reprint). (SCI, impact factor 0.805, rank ENGINEERING, CIVIL 73/125) 
  • Y.-C. Chu, G.-J. Lee, C.-Y. Chen, S.-H. Ma, J.-J. Wu, T.-L. Horng, K.-H. Chen, Y.-W. Huang, L.-Y. Lai, J.-H. Chen*, 2015, "Improved Design of UV- and Blue-Light-Inhibited White Light-Emitting Diode," IEEE Photonics Journal,7(4):1600806,(accepted July 2015, published August 2015), (reprint). (SCI, impact factor 2.209, rank ENGINEERING, ELECTRICAL & ELECTRONIC  49/249)
  • Wei Hsieh, Tzyy-Leng Allen Horng, Hsin-Chieh Huang, Hsisheng Teng*, 2015, "Facile simulation of carbon with wide pore size distribution for electric double-layer capacitance based on Helmholtz model," Journal of Materials Chemistry A, 3:16535-16543,(accepted July 2015, published August 2015), (reprint). (SCI, impact factor 7.443, rank ENERGY & FUELS  5/89, cited by 2)   
  • M. J. Chern, E. Odhiambo*, T. L. Horng, A. G. L. Borthwick,2016, "Numerical simulation of vibration of horizontal cylinder induced by progressive waves," Fluid Dynamics Research, 48:015508, (accepted November 2015, published January 2016),  (reprint). (SCI, impact factor 0.990, rank MECHANICS  88/137)
  • M. J. Chern*, Y. L. Chen, C. B. Liao, T. L. Horng,2017, "Numerical study for oscillatory flow past three-cylinder array in regular triangle arrangement using direct-forcing immersed boundary method," Journal of Taiwan Society of Naval Architects and Marine Engineers, 36(2):51-67, (published May 2017),  (reprint). (EI)
  • Cheng-Ying Chou*, Wan-I Chang, Tzyy-Leng Horng*, Win-Li Lin, 2017, "Numerical modeling of nanodrug distribution in tumors with heterogeneous vasculature," PLoS ONE, 12(12):e0189802, (published Dec 2017), (reprint). (SCI,  impact factor 3.234, rank MULTIDISCIPLINARY SCIENCES 9/57)
  • Tzyy-Leng Horng*, Ping-Hsuan Tsai, and Tai-Chia Lin, 2017, "Modification of Bikerman model with specific ion sizes," Mol. Based Math. Biol., 5:142–149, (reprint).
  • M. J. Chern*, G. T. Lu, Y. H. Kuan, S. Charkraborty, G. Nugroho, C. B. Liao, T. L. Horng,2018, "Numerical study for vortex-induced vibration of circular cylinder adjacent to plane boundary using direct-forcing immersed boundary method," Journal of Mechanics, 34(2):177-191, (published April 2018),  (reprint). (SCI, impact factor 0.819, rank MECHANICS 112/133)

* : corresponding author. Citation number based on Google Scholar.


Book Reports

  • A.T.L. Horng, 1995, "Chebyshev Collocation Method on Solving Stability of A Liquid Layer Folwing Down an Inclined Plane ", in The Mecbanics of Thin Film Coatings , p.95-106, edited by P.H. Gaskell, M.D. Savage, and J.L. Summers, World Scientific, Singapore (reprint).
  • Chao-Nien Chen, Tzyy-Leng Horng, Daniel Lee, Chen-Hsing Tsai, 2009, "A Note on Reaction-Diffusion Systems with Skew-Gradient Structure ", in Recent Progress on Reaction-Diffusion Systems and Viscosity Solutions, p.31-48, edited by Yihong Du, Hitoshi Ishii, and Wei-ueh Lin, World Scientific, Singapore (reprint).
  • Huang-Wen Huang and Tzyy-Leng Horng, 2015, "Bioheat transfer and thermal heating for tumor treatment", in Heat Transfer and Fluid Flow in Biological Processes, p.1-42, edited by Sid M. Becker and Andrey V. Kuznestov, Academic Press, USA (reprint).


Technical Reports

  • Jerry M. Chen and Tzyy-Leng Horng, 2002, "Modeling and Parameter Design of Aspirative Air Bag Inflator (II) "
  • Jerry M. Chen and Tzyy-Leng Horng, 2001, "Modeling and Parameter Design of Aspirative Air Bag Inflator (I) "



  • Computer Aided Instruction and Learning for Mathematics Website, 2003.
  • MATLAB Linear Algebra CAI Toolbox, 2001.
  • MATLAB Numerical Methods and Analysis CAI Toolbox, 1999.


Research & Teaching

Teaching at ISTM in Fall 2018/Spring 2019

  • Ordinary Differential Equations (FCU-Purdue Program Year 2)



  • Numerical Analysis and Scientific Computing
  • Spectral and Pseudospectral Methods
  • Computational Fluid Dynamics and Heat Transfer
  • Immerse Boundary Method
  • Vortex Ring Dynamics
  • Bose-Einstein Condensation , Super-Fluid, Super-Solid
  • Option Pricing
  • Simulation of Thermal Therapy on Tumor
  • Microfluidics
  • Design and Simulation of Aspirative Air Bag
  • Simulation of Chemical Mechanical Polishing and Planarization
  • Modeling and Simulation of Cardiac Arrhy-thmias
  • Biological Pattern Formation
  • Modeling and Bifurcation Analysis of Neurona
  • Wave Function Engineering of Quantum Wells and Superlattice
  • Soliton in Optic Fiber
  • Flow Instabilities
  • Flow and Structure Interaction
  • Free Surface Flows
  • Medical Image Segmentation
  • Simulation of Respiratory Flow in the Airway.
  • Ion Channel, Poisson-Nernst-Planck Equations



  • Calculus
  • Numerical Methods and Analysis
  • Advanced topics for applied mathematics
  • Hyperbolic PDEs
  • Ordinary Differential Equations
  • Advanced Topics for Numerical Methods
  • Mathematical Biology