IDEAS home Printed from https://ideas.repec.org/p/hhs/kthind/2014_006.html
   My bibliography  Save this paper

Finite Element Model of the Innovation Diffusion: An Application to Photovoltaic Systems

Author

Listed:
  • Karakaya, Emrah

    (Technical University of Madrid & KTH Royal Institute of Technology)

Abstract

This paper presents a Finite Element Model, which has been used for forecasting the diffusion of innovations in time and space. Unlike conventional models used in diffusion literature, the model considers spatial heterogeneity. The implementation steps of the model are explained by applying it to the case of diffusion of photovoltaic systems in a local region in southern Germany. The applied model is based on a parabolic partial differential equation that describes the diffusion ratio of photovoltaic systems in a given region over time. The results of the application suggest that the Finite Element Model could be a powerful tool to improve our understanding on the diffusion of innovations as a simultaneous space-time process. For future research, model limitations and possible extensions are also discussed.

Suggested Citation

  • Karakaya, Emrah, 2014. "Finite Element Model of the Innovation Diffusion: An Application to Photovoltaic Systems," INDEK Working Paper Series 2014/6, Royal Institute of Technology, Department of Industrial Economics and Management.
    • Handle: RePEc:hhs:kthind:2014_006
    as

    Download full text from publisher

    File URL: https://static.sys.kth.se/itm/wp/indek/indekwp6.pdf
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Yang, Hai & Yagar, Sam & Iida, Yasunori, 1994. "Traffic assignment in a congested discrete/ continuous transportation system," Transportation Research Part B: Methodological, Elsevier, vol. 28(2), pages 161-174, April.
    2. McGrattan, Ellen R., 1996. "Solving the stochastic growth model with a finite element method," Journal of Economic Dynamics and Control, Elsevier, vol. 20(1-3), pages 19-42.
    3. Li, Jenny X., 1998. "Numerical analysis of a nonlinear operator equation arising from a monetary model," Journal of Economic Dynamics and Control, Elsevier, vol. 22(8-9), pages 1335-1351, August.
    4. Adam G. Dunn & Blanca Gallego, 2010. "Diffusion of Competing Innovations: The Effects of Network Structure on the Provision of Healthcare," Journal of Artificial Societies and Social Simulation, Journal of Artificial Societies and Social Simulation, vol. 13(4), pages 1-8.
    5. Beise, Marian, 2004. "Lead markets: country-specific drivers of the global diffusion of innovations," Research Policy, Elsevier, vol. 33(6-7), pages 997-1018, September.
    6. Kwan, Calvin Lee, 2012. "Influence of local environmental, social, economic and political variables on the spatial distribution of residential solar PV arrays across the United States," Energy Policy, Elsevier, vol. 47(C), pages 332-344.
    7. S. C. Wong & S. H. Sun, 2001. "A combined distribution and assignment model for continuous facility location problem," The Annals of Regional Science, Springer;Western Regional Science Association, vol. 35(2), pages 267-281.
    8. Hai Yang & S. C. Wong, 2000. "A Continuous Equilibrium Model for Estimating Market Areas of Competitive Facilities with Elastic Demand and Market Externality," Transportation Science, INFORMS, vol. 34(2), pages 216-227, May.
    9. Frank M. Bass & Trichy V. Krishnan & Dipak C. Jain, 1994. "Why the Bass Model Fits without Decision Variables," Marketing Science, INFORMS, vol. 13(3), pages 203-223.
    10. Beise, Marian & Rennings, Klaus, 2005. "Lead markets and regulation: a framework for analyzing the international diffusion of environmental innovations," Ecological Economics, Elsevier, vol. 52(1), pages 5-17, January.
    11. Haynes, Kingsley E. & Mahajan, Vijay & White, Gerald M., 1977. "Innovation diffusion: A deterministic model of space-time integration with physical analog," Socio-Economic Planning Sciences, Elsevier, vol. 11(1), pages 25-29.
    12. Kazunori Shinohara & Hiroshi Okuda, 2010. "Dynamic Innovation Diffusion Modelling," Computational Economics, Springer;Society for Computational Economics, vol. 35(1), pages 51-62, January.
    13. Golbabai, A. & Ballestra, L.V. & Ahmadian, D., 2013. "Superconvergence of the finite element solutions of the Black–Scholes equation," Finance Research Letters, Elsevier, vol. 10(1), pages 17-26.
    14. Rama Cont & Nicolas Lantos & Olivier Pironneau, 2011. "A reduced basis for option pricing," Post-Print hal-00522410, HAL.
    15. Nigel Meade & Towhidul Islam, 1998. "Technological Forecasting---Model Selection, Model Stability, and Combining Models," Management Science, INFORMS, vol. 44(8), pages 1115-1130, August.
    16. Kobos, Peter H. & Erickson, Jon D. & Drennen, Thomas E., 2006. "Technological learning and renewable energy costs: implications for US renewable energy policy," Energy Policy, Elsevier, vol. 34(13), pages 1645-1658, September.
    17. Frank M. Bass, 1969. "A New Product Growth for Model Consumer Durables," Management Science, INFORMS, vol. 15(5), pages 215-227, January.
    18. Higgins, Andrew & McNamara, Cheryl & Foliente, Greg, 2014. "Modelling future uptake of solar photo-voltaics and water heaters under different government incentives," Technological Forecasting and Social Change, Elsevier, vol. 83(C), pages 142-155.
    19. Kumar Muthuraman & Sunil Kumar, 2006. "Multidimensional Portfolio Optimization With Proportional Transaction Costs," Mathematical Finance, Wiley Blackwell, vol. 16(2), pages 301-335, April.
    20. Ajzen, Icek, 1991. "The theory of planned behavior," Organizational Behavior and Human Decision Processes, Elsevier, vol. 50(2), pages 179-211, December.
    21. Wong, S. C., 1998. "Multi-commodity traffic assignment by continuum approximation of network flow with variable demand," Transportation Research Part B: Methodological, Elsevier, vol. 32(8), pages 567-581, November.
    22. S. Wong & Y. Du & L. Sun & B. Loo, 2006. "Sensitivity analysis for a continuum traffic equilibrium problem," The Annals of Regional Science, Springer;Western Regional Science Association, vol. 40(3), pages 493-514, August.
    23. Berger, Thomas, 2001. "Agent-based spatial models applied to agriculture: a simulation tool for technology diffusion, resource use changes and policy analysis," Agricultural Economics, Blackwell, vol. 25(2-3), pages 245-260, September.
    24. Popp, David & Hascic, Ivan & Medhi, Neelakshi, 2011. "Technology and the diffusion of renewable energy," Energy Economics, Elsevier, vol. 33(4), pages 648-662, July.
    25. Baccarin, Stefano, 2009. "Optimal impulse control for a multidimensional cash management system with generalized cost functions," European Journal of Operational Research, Elsevier, vol. 196(1), pages 198-206, July.
    26. Ho, H.W. & Wong, S.C. & Yang, Hai & Loo, Becky P.Y., 2005. "Cordon-based congestion pricing in a continuum traffic equilibrium system," Transportation Research Part A: Policy and Practice, Elsevier, vol. 39(7-9), pages 813-834.
    27. Hatem Ben-Ameur & Michèle Breton & Pierre L'Ecuyer, 2002. "A Dynamic Programming Procedure for Pricing American-Style Asian Options," Management Science, INFORMS, vol. 48(5), pages 625-643, May.
    28. Mesak, HI & Coleman, RW, 1992. "Modeling the effect of subsidized pricing policy on new product diffusion," Omega, Elsevier, vol. 20(3), pages 303-312, May.
    29. Ho, H.W. & Wong, S.C. & Loo, Becky P.Y., 2006. "Combined distribution and assignment model for a continuum traffic equilibrium problem with multiple user classes," Transportation Research Part B: Methodological, Elsevier, vol. 40(8), pages 633-650, September.
    30. Rambeerich, N. & Tangman, D.Y. & Lollchund, M.R. & Bhuruth, M., 2013. "High-order computational methods for option valuation under multifactor models," European Journal of Operational Research, Elsevier, vol. 224(1), pages 219-226.
    31. Barone-Adesi, Giovanni & Bermudez, Ana & Hatgioannides, John, 2003. "Two-factor convertible bonds valuation using the method of characteristics/finite elements," Journal of Economic Dynamics and Control, Elsevier, vol. 27(10), pages 1801-1831, August.
    32. Guseo, Renato & Guidolin, Mariangela, 2015. "Heterogeneity in diffusion of innovations modelling: A few fundamental types," Technological Forecasting and Social Change, Elsevier, vol. 90(PB), pages 514-524.
    33. José Cao-Alvira, 2010. "Finite Elements in the Presence of Occasionally Binding Constraints," Computational Economics, Springer;Society for Computational Economics, vol. 35(4), pages 355-370, April.
    34. Jiang, Yanqun & Wong, S.C. & Ho, H.W. & Zhang, Peng & Liu, Ruxun & Sumalee, Agachai, 2011. "A dynamic traffic assignment model for a continuum transportation system," Transportation Research Part B: Methodological, Elsevier, vol. 45(2), pages 343-363, February.
    35. Elmar Kiesling & Markus Günther & Christian Stummer & Lea Wakolbinger, 2012. "Agent-based simulation of innovation diffusion: a review," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 20(2), pages 183-230, June.
    36. Meade, Nigel & Islam, Towhidul, 2006. "Modelling and forecasting the diffusion of innovation - A 25-year review," International Journal of Forecasting, Elsevier, vol. 22(3), pages 519-545.
    37. Zhu, Song-Ping & Chen, Wen-Ting, 2013. "An inverse finite element method for pricing American options," Journal of Economic Dynamics and Control, Elsevier, vol. 37(1), pages 231-250.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Karakaya, Emrah, 2016. "Finite Element Method for forecasting the diffusion of photovoltaic systems: Why and how?," Applied Energy, Elsevier, vol. 163(C), pages 464-475.
    2. Elmar Kiesling & Markus Günther & Christian Stummer & Lea Wakolbinger, 2012. "Agent-based simulation of innovation diffusion: a review," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 20(2), pages 183-230, June.
    3. Kumar, Rajeev Ranjan & Guha, Pritha & Chakraborty, Abhishek, 2022. "Comparative assessment and selection of electric vehicle diffusion models: A global outlook," Energy, Elsevier, vol. 238(PC).
    4. Constanza Fosco, 2012. "Spatial Difusion and Commuting Flows," Documentos de Trabajo en Economia y Ciencia Regional 30, Universidad Catolica del Norte, Chile, Department of Economics, revised Sep 2012.
    5. Krishnan, Trichy V. & Feng, Shanfei & Jain, Dipak C., 2023. "Peak sales time prediction in new product sales: Can a product manager rely on it?," Journal of Business Research, Elsevier, vol. 165(C).
    6. Kurdgelashvili, Lado & Shih, Cheng-Hao & Yang, Fan & Garg, Mehul, 2019. "An empirical analysis of county-level residential PV adoption in California," Technological Forecasting and Social Change, Elsevier, vol. 139(C), pages 321-333.
    7. Guseo, Renato & Schuster, Reinhard, 2021. "Modelling dynamic market potential: Identifying hidden automata networks in the diffusion of pharmaceutical drugs," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 581(C).
    8. Ho, H.W. & Wong, S.C. & Loo, Becky P.Y., 2006. "Combined distribution and assignment model for a continuum traffic equilibrium problem with multiple user classes," Transportation Research Part B: Methodological, Elsevier, vol. 40(8), pages 633-650, September.
    9. Yan-Qun Jiang & S.C. Wong & Peng Zhang & Keechoo Choi, 2017. "Dynamic Continuum Model with Elastic Demand for a Polycentric Urban City," Transportation Science, INFORMS, vol. 51(3), pages 931-945, August.
    10. Liu, Tian-Liang & Huang, Hai-Jun & Yang, Hai & Zhang, Xiaoning, 2009. "Continuum modeling of park-and-ride services in a linear monocentric city with deterministic mode choice," Transportation Research Part B: Methodological, Elsevier, vol. 43(6), pages 692-707, July.
    11. Chumnumpan, Pattarin & Shi, Xiaohui, 2019. "Understanding new products’ market performance using Google Trends," Australasian marketing journal, Elsevier, vol. 27(2), pages 91-103.
    12. Zhang, Nan & Hwang, Bon-Gang & Lu, Yujie & Ngo, Jasmine, 2022. "A Behavior theory integrated ANN analytical approach for understanding households adoption decisions of residential photovoltaic (RPV) system," Technology in Society, Elsevier, vol. 70(C).
    13. Byrka, Katarzyna & Jȩdrzejewski, Arkadiusz & Sznajd-Weron, Katarzyna & Weron, Rafał, 2016. "Difficulty is critical: The importance of social factors in modeling diffusion of green products and practices," Renewable and Sustainable Energy Reviews, Elsevier, vol. 62(C), pages 723-735.
    14. Furlan, Claudia & Guidolin, Mariangela & Guseo, Renato, 2016. "Has the Fukushima accident influenced short-term consumption in the evolution of nuclear energy? An analysis of the world and seven leading countries," Technological Forecasting and Social Change, Elsevier, vol. 107(C), pages 37-49.
    15. Shi, Xiaohui & Chumnumpan, Pattarin, 2019. "Modelling market dynamics of multi-brand and multi-generational products," European Journal of Operational Research, Elsevier, vol. 279(1), pages 199-210.
    16. van Blommestein, Kevin & Daim, Tugrul U. & Cho, Yonghee & Sklar, Paul, 2018. "Structuring financial incentives for residential solar electric systems," Renewable Energy, Elsevier, vol. 115(C), pages 28-40.
    17. Xiao, Yu & Han, Jingti, 2016. "Forecasting new product diffusion with agent-based models," Technological Forecasting and Social Change, Elsevier, vol. 105(C), pages 167-178.
    18. Ho, H.W. & Wong, S.C. & Yang, Hai & Loo, Becky P.Y., 2005. "Cordon-based congestion pricing in a continuum traffic equilibrium system," Transportation Research Part A: Policy and Practice, Elsevier, vol. 39(7-9), pages 813-834.
    19. Huang, Ling & Wong, S.C. & Zhang, Mengping & Shu, Chi-Wang & Lam, William H.K., 2009. "Revisiting Hughes' dynamic continuum model for pedestrian flow and the development of an efficient solution algorithm," Transportation Research Part B: Methodological, Elsevier, vol. 43(1), pages 127-141, January.
    20. Felix Groba & Barbara Breitschopf, 2013. "Impact of Renewable Energy Policy and Use on Innovation: A Literature Review," Discussion Papers of DIW Berlin 1318, DIW Berlin, German Institute for Economic Research.

    More about this item

    Keywords

    Innovation; Adoption; Spatiotemporal; prediction; solar photovoltaics;
    All these keywords.

    JEL classification:

    • C02 - Mathematical and Quantitative Methods - - General - - - Mathematical Economics
    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques
    • O33 - Economic Development, Innovation, Technological Change, and Growth - - Innovation; Research and Development; Technological Change; Intellectual Property Rights - - - Technological Change: Choices and Consequences; Diffusion Processes
    • Q55 - Agricultural and Natural Resource Economics; Environmental and Ecological Economics - - Environmental Economics - - - Environmental Economics: Technological Innovation
    • R00 - Urban, Rural, Regional, Real Estate, and Transportation Economics - - General - - - General

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:hhs:kthind:2014_006. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Vardan Hovsepyan (email available below). General contact details of provider: https://edirc.repec.org/data/iikthse.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.