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Function for Heun's differential equation
the local Heun function H ℓ ( a , q ; α , β , γ , δ ; z ) {\displaystyle H\ell (a,q;\alpha ,\beta ,\gamma ,\delta ;z)} is the solution of Heun's differential
Heun_function
German mathematician (1859–1929)
German mathematician who introduced Heun's equation, Heun functions, and Heun's method. Karl Heun studied mathematics and philosophy at the University of
Karl_Heun
Type of functions, in mathematical analysis
class of hypergeometric functions. Examples of special functions that are holonomic but not hypergeometric include the Heun functions. Examples of holonomic
Holonomic_function
Procedure for solving ODEs
In mathematics and computational science, Heun's method may refer to the improved or modified Euler's method (that is, the explicit trapezoidal rule),
Heun's_method
Hermann Hankel: Hankel function Heine: Heine functions Charles Hermite: Hermite polynomials Karl L. W. M. Heun (1859 – 1929): Heun's equation J. Horn: Horn
List of eponyms of special functions
List_of_eponyms_of_special_functions
Solutions of Lamé's equation
} which after a change of variable becomes a special case of Heun's equation. A more general form of Lamé's equation is the ellipsoidal equation
Lamé_function
and elliptic and theta functions Equations of mathematical physics, including continuous and discrete Painlevé, Lamé and Heun equations Transforms and
Bateman_Manuscript_Project
original (PDF) on 8 July 2011. "Om LTH". LTH. Retrieved 23 October 2011. Heun, Helga (28 February 2022). "The will to achieve gender equality and equal
Faculty of Engineering, Lund University
Faculty_of_Engineering,_Lund_University
Algorithms in numerical analysis
method for the corrector step. A simple predictor–corrector method (known as Heun's method) can be constructed from the Euler method (an explicit method) and
Predictor–corrector_method
Family of implicit and explicit iterative methods
{1}{2}}} gives the midpoint method, α = 1 {\displaystyle \alpha =1} is Heun's method, and α = 2 3 {\displaystyle \alpha ={\tfrac {2}{3}}} is Ralston's
Runge–Kutta_methods
Technique for the generative modeling of a continuous probability distribution
any of the numerical integration methods, such as Euler–Maruyama method, Heun's method, linear multistep methods, etc. Just as in the discrete case, one
Diffusion_model
Type of ion channel transmembrane protein
galantamine, rivastigmine and memantine (review): final appraisal determination Heun R, Corral RM, Ahokas A, Nicolini H, Teixeira JM, Dehelean P (2013). "1643
Ligand-gated_ion_channel
2019 South Korean media sex scandal
from the original on March 28, 2019. Retrieved March 20, 2019. Kim, Jae-heun (March 10, 2019). "Big Bang's Seungri booked on sex bribery charge". The
Burning_Sun_scandal
Concept in differential equation mathematics
A solution is the hypergeometric function. Arscott, F. M. (1995). "Heun's Equation". In Ronveaux, A. (ed.). Heun's Differential Equations. Oxford University
Regular_singular_point
{\displaystyle {\begin{array}{c|cc}0&0&0\\1/2&1/2&0\\\hline &0&1\\\end{array}}} Heun's method is a second-order method with two stages. It is also known as the
List_of_Runge–Kutta_methods
Government agency of South Korea
Bulletin. "한국관광공사: 역대 CEO". knto.or.kr (in Korean). Retrieved 2025-09-30. Jae-heun, Kim (2025-07-24). "Actor Park Bo-gum new face of Korea's tourism". The Korea
Korea_Tourism_Organization
Protein family
Ludwig M, Schulte A, Ptok U, Jessen F, von Bergmann K, Rao ML, Maier W, Heun R (2002). "Polymorphism in the cholesterol 24S-hydroxylase gene is associated
Cholesterol_24-hydroxylase
South Korean art director (born 1979)
Archived from the original on May 17, 2024. Retrieved May 18, 2024. Kim, Jae-heun (May 13, 2024). "Ador CEO's fate to be decided on May 17". The Korea Herald
Min_Hee-jin
Protein found in humans
(1): 78–88. doi:10.1086/498851. PMC 1380225. PMID 16385451. von Trotha KT, Heun R, Schmitz S, Lütjohann D, Maier W, Kölsch H (July 2006). "Influence of lysosomal
Lysosomal_lipase
South Korean public research university
improvement. Kyoungchul Kong, Mechanical engineer, entrepreneur and academic Heun Lee, identified mechanism behind hydrogen storage in ice particles Ji-O Lee
KAIST
Failures to secure dangerous animals and pathogens
Retrieved 2025-09-20. Lee, Changhwan; Jang, Eun Jung; Kwon, Donghyok; Choi, Heun; Park, Jung Wan; Bae, Geun-Ryang (7 April 2016). "Laboratory-acquired dengue
List of laboratory biosecurity incidents
List_of_laboratory_biosecurity_incidents
British AI researcher (born 1976)
Archived from the original on 2 July 2022. Retrieved 11 June 2020. Kahng, Jee Heun (15 March 2016). "Google artificial intelligence program beats S. Korean
Demis_Hassabis
Characteristic of human females
Young; Chang, Yoosoo; Ahn, Jiin; Yun, Ji-Sup; Park, Yong Lai; Park, Chan Heun; Shin, Hocheol; Ryu, Seungho (30 July 2020). "Menopausal Transition, Body
Female_body_shape
2006 film by Bong Joon Ho
the original on November 1, 2024. Retrieved February 17, 2025. Kim, Jae-heun (February 15, 2017). "Korean films influenced US monster movie". The Korea
The_Host_(2006_film)
and S prior to beginning integration. Other more refined methods such as Heun or Runge-Kutta and implicit Euler can be implemented but are way more hardware
Digital_differential_analyzer
(after Edward Burr Van Vleck) and S is called a Heine–Stieltjes polynomial. Heun polynomials are the special cases of Stieltjes polynomials when the differential
Heine–Stieltjes_polynomials
Type of thoroughfare
p. 254. Slaughter 2021, 3:04. Slaughter 2021, 6:00. Van Antwerp, Jeremy; Heun, Matthew Kuperus (2022). A Framework for Sustainability Thinking: A Student's
Stroad
Protein found in humans
PMID 15078902. Kölsch H, Ptok U, Majores M, Schmitz S, Rao ML, Maier W, Heun R (2004). "Putative association of polymorphism in the mannose 6-phosphate
Cation-dependent mannose-6-phosphate receptor
Cation-dependent_mannose-6-phosphate_receptor
United States historic place
was led by Mother Agnes Dwight, Sister Michael Skelley, Sister Magdalen Heun, Sister Raphael Baker, Sister Marie Schuman, and Sister Clare Lafferty. Social
Regina_Coeli_Monastery
South Korean multinational corporation
half of 2025". Music Business Worldwide. Retrieved September 26, 2025. Jae-heun, Kim (September 23, 2025). "BTS' agency eyes India's 1.4 billion market with
Hybe
Nonspecific long-lasting anxiety
190–211. doi:10.1002/da.20653. PMID 20099273. S2CID 12981577. Barkow K, Heun R, Wittchen HU, Üstün TB, Gänsicke M, Maier W (April 2004). "Mixed anxiety–depression
Generalized_anxiety_disorder
British mathematician
Differential Equations 1987, University of Dundee Numerical Analysis Reports Heun's Differential Equations, Oxford University Press, 1995. (contributor) "Chronicle"
Felix_Arscott
Numeric solution for differential equations
symplectic integrator. Note that the modified Euler method can refer to Heun's method, for further clarity see List of Runge–Kutta methods. The name of
Midpoint_method
Liskovykh, Mikhail A.; Barrey, Evelyne J.; Larionov, Vladimir; Miga, Karen H.; Heun, Patrick; Black, Ben E. (2019-07-25). "Human Artificial Chromosomes that
Human_artificial_chromosome
this becomes a Heun equation with singular points at x = − 1 , 0 , + 1 {\displaystyle x=-1,0,+1} . Based on the known solutions of the Heun equation, we
Spherium
Large stone used to build a structure or monument
Tepe Research Staff. Blog entry 18. Retrieved 2019-08-04. Dietrich, O.; Heun, M.; Notroff, J.; Schmidt, K.; Zarnkow, M. (2012). "The role of cult and
Megalith
Protein used in lipid metabolism
124–129. doi:10.3132/dvdr.2007.030. PMID 17654446. S2CID 23793589. Vollbach H, Heun R, Morris CM, Edwardson JA, McKeith IG, Jessen F, et al. (September 2005)
Apolipoprotein_AI
Webtoon hosting service
Retrieved July 25, 2020. "Doctor Frost". IMDb. Retrieved July 25, 2020. Kim, Jae-heun (May 13, 2015). "Yeo Jin-goo promises romance in "Orange Marmalade"". The
Webtoon_(platform)
Artificial intelligence that plays Go
Archived from the original on 21 March 2016. Retrieved 18 March 2016. JEE HEUN KAHNG; SE YOUNG LEE (15 March 2016). "Google artificial intelligence program
AlphaGo
Protein-coding gene in the species Homo sapiens
Holstege H, Kornhuber J, Peters O, Naj AC, Chouraki V, Bellenguez C, Gerrish A, Heun R, Frölich L, Hüll M, Buscemi L, Herms S, Kölsch H, Scheltens P, Breteler
SUCLG2
world. Oxford: Blackwell Publishers. pp. 144–160. Oliver Dietrich, Manfred Heun, Jens Notroff, Klaus Schmidt and Martin Zarnkow, "The role of cult and feasting
Neolithic_in_the_Near_East
South Korean popular music genre
from the original on March 14, 2023. Retrieved March 14, 2023. Kim, Jae-heun (February 18, 2019). "TV guidelines on 'look-alike' K-pop singers spark controversy"
K-pop
initial-value problems Midpoint method — a second-order method with two stages Heun's method — either a second-order method with two stages, or a third-order
List of numerical analysis topics
List_of_numerical_analysis_topics
Guidance relationship
Credibility. San Francisco: Jossey Bass. pp. 155. ISBN 9781555425500. Ensher, E.; Heun, C.; Blanchard, A. (2003). "Online mentoring and computer-mediated communication:
Mentorship
S2CID 93787426. Rai, Prabhakar; Majhi, Sanjit Manohar; Yu, Yeon-Tae; Lee, Jong-Heun (2015). "Noble metal@metal oxide semiconductor core@shell nano-architectures
Energy applications of nanotechnology
Energy_applications_of_nanotechnology
Molecular biologist
strand breaks in yeast". Cell. 97: 621–633. doi:10.1016/S0092-8674(00)80773-4 Heun, P.; Laroche, T.; Shimada, K.; Furrer, P.; Gasser, S. M. (2001). "Chromosomal
Susan_M._Gasser
Euler, implicit Midpoint, Crank-Nicolson, SDIRK. Embedded explicit methods: Heun-Euler, Bogacki-Shampine, Dopri, Fehlberg, Cash-Karp. implicit-euler explicit-euler
List of finite element software packages
List_of_finite_element_software_packages
archives after the Second World War. Translated by Seyer, D. CUP. pp. 219 ff. Heun, Werner (2011). The Constitution of Germany. Hart. Gesetz über das Staatsoberhaupt
Legal_status_of_Germany
; Siewert, C. E. (2004). "On computing the Chapman–Enskog and Burnett functions". Journal of Quantitative Spectroscopy and Radiative Transfer. 86 (1):
List of scientific equations named after people
List_of_scientific_equations_named_after_people
Japanese mathematician and professor
equivalent to a confluent Heun differential equation, and NCHO is considered as a covering model of QRM via the confluence process of the Heun equation [25, 29]
Masato_Wakayama
Capital of Baden-Württemberg, Germany
Landeshauptstadt Stuttgart (in German). Retrieved 9 January 2024. Schlaich, Heckel & Heun 1997, p. 28. "Religiöse Vielfalt in einer wachsenden Stadt – Kirche und Religion
Stuttgart
Architectural style
Elmslie Hugh M. G. Garden Marion Mahony Griffin Walter Burley Griffin Arthur Heun John H. Howe Jens Jensen Henry John Klutho George Washington Maher Mason
Prairie_School
equations List of named differential equations Vallée, Olivier (2004). Airy functions and applications to physics. Internet Archive. Hackensack, NJ : World
List of linear ordinary differential equations
List_of_linear_ordinary_differential_equations
the previous timestep to generate a more accurate result. For instance, Heun's Method (second order) averages the velocity from the current and previous
Gipps'_model
Smart payment card standard
"Amex joins Visa in postponing US gas EMV migration". 5 May 2020. David Heun (10 September 2012). "MasterCard Brings EMV Chip-Card Liability Policy to
EMV
South Korean businessperson (born 1982)
marketing technology company, Orbit, in an effort to stabilize its business. Jae-heun, Kim (2026-08-04). "The woman behind a K-pop empire — and its stunning collapse"
Cha_Ga-won
South Korean actor (born 1986)
from the original on October 3, 2015. Retrieved October 6, 2015. Kim, Jae-heun (October 2, 2015). "Yoo Ah-in seeks another success". The Korea Times. Archived
Yoo_Ah-in
Numerical problem-solving method
After a group of multi-step methods was presented in 1883, Carl Runge, Karl Heun and Wilhelm Kutta developed significant improvements to Euler's method around
One-step_method
Platform. Archived from the original on 2014-05-31. Retrieved 2013-07-21. Suh Heun-gang, Ahn Hong-beom. "Fifty Years of Endeavors for Preservation and Transmission"
Heritage preservation in South Korea
Heritage_preservation_in_South_Korea
Genetic disorder resulting in abnormal enamel
PMID 27412008. Seymen, Figen; Kim, Youn Jung; Lee, Ye Ji; Kang, Jenny; Kim, Tak-Heun; Choi, Hwajung; Koruyucu, Mine; Kasimoglu, Yelda; Tuna, Elif Bahar; Gencay
Amelogenesis_imperfecta
reduced error compared to the Euler scheme (see e.g. Milstein, Runge-Kutta or Heun's method) these almost always come at an efficiency cost, requiring more computation
Leimkuhler–Matthews_method
Biological process
nucleus is far smaller than the number of genomic replication forks. P. Heun et al. tracked GFP-tagged replication foci in budding yeast cells and revealed
DNA_replication
Mammalian protein found in Homo sapiens
Brown K, Kehoe PG, Barber R, Coto E, Alvarez V, Deloukas P, Gwilliam R, Heun R, Kölsch H, Mateo I, Oulhaj A, Arias-Vásquez A, Schuur M, Aulchenko YS,
Dopamine_beta-hydroxylase
South Korean singer (born 1989)
Osen (in Korean). Retrieved June 15, 2026 – via The Chosun Ilbo. Kim, Jae-heun (June 21, 2026). "Secret bets on nostalgia, reinvention in comeback". The
Jun_Hyo-seong
Energy that responsibly meets social, economic, and environmental needs
Organization 2021, p. 11. Brockway, Paul E.; Sorrell, Steve; Semieniuk, Gregor; Heun, Matthew Kuperus; Court, Victor (May 2021). "Energy efficiency and economy-wide
Sustainable_energy
South Korean art of the Minjung movement
(born 1955) Choi Byung Soo (born 1960) Shin Hak-chul Joo Jae-hwan Kim Jeong-heun Min Jeong-ki Kim Yong-tae Minjung Gwangju Uprising (Park, Ki-woong. “Korean
Minjung_art
Increase in consumption following energy or resource savings
Energy Research Centre. Brockway, Paul E.; Sorrell, Steve; Semieniuk, Gregor; Heun, Matthew Kuperus; Court, Victor (May 2021). "Energy efficiency and economy-wide
Rebound_effect_(conservation)
ISSN 0002-7820. Park, Hwi-Yeol; Ahn, Cheol-Woo; Song, Hyun-Cheol; Lee, Jong-Heun; Nahm, Sahn; Uchino, Kenji; Lee, Hyeung-Gyu; Lee, Hwack-Joo (2006-08-07)
List of piezoelectric materials
List_of_piezoelectric_materials
South Korean boy band
from the original on March 28, 2019. Retrieved March 24, 2016. Kim, Jae-heun (February 28, 2016). "BTOB sings about spring in 'Remember That'". The Korea
BtoB_(band)
Borough in Essex County, New Jersey, US
is governed by a directly elected county executive, with legislative functions performed by the Board of County Commissioners. As of 2025[update], the
Caldwell,_New_Jersey
American educator
roles, functions, and behavior of women on boards of education in DuPage County, Illinois (Thesis). Loyola University Chicago. OCLC 10014966. Heun, Dave
Stephanie_Pace_Marshall
South Korean branch of Billboard
Korea to Officially Launch on Aug. 27". KBS World. August 22, 2024. Kim, Jae-heun (July 4, 2024). "Third launch of Billboard Korea delayed". The Korea Herald
Billboard_Korea
Flying robot for planetary exploration
(abstract at smithsonian database, retrieved 13 May 2015) Jack A. Jones and Matt Heun [Montgolfiere Balloon Aerobots for Jupiter’s Atmosphere (Abstract)] Jet Propulsion
Aerobot
InterPro Family
www.ebi.ac.uk. Retrieved 2025-12-01. Anselm E, Thomae AW, Jeyaprakash AA, Heun P (November 2018). "Oligomerization of Drosophila Nucleoplasmin-Like Protein
Nucleoplasmin
German physician, cardiologist and university professor (born 1944)
Jürgen Flöge, Jan Galle, Helmut Geiger, Bernd Grabensee, Fokko de Haan, Klaus Heun, Katrin Ivens, Werner Kleophas, Arno Krian, Johannes Kroll, Bernd Kutkuhn
Günter_Breithardt
South Korean science award
synthetic method for Daumone, a longevity-inducing nematode September Lee Heun (이흔) KAIST Biochemical engineering Elucidation of hydrogen storage phenomena
Scientist_of_the_Month
German radiologist
Brain. 126 (Pt 10): 2121–2138. doi:10.1093/brain/awg226. PMID 12902310. Heun, R.; Klose, U.; Jessen, F.; et al. (1999). "Functional MRI of cerebral activation
Wolfgang_Grodd
travel, tourism, insurance
HEUN FUNCTION
HEUN FUNCTION
HEUN FUNCTION
HEUN FUNCTION
HEUN FUNCTION
HEUN FUNCTION
HEUN FUNCTION
HEUN FUNCTION
HEUN FUNCTION
travel, tourism, insurance