Abstract
We present an extension to the graph-transformation based programming language XL that allows easy specification and solution of differential equations on graphs.
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Federl, P., Prusinkiewicz, P.: Solving differential equations in developmental models of multicellular structures expressed using L-systems. In: Bubak, M., van Albada, G.D., Sloot, P.M.A., Dongarra, J. (eds.) ICCS 2004. LNCS, vol. 3037, pp. 65–72. Springer, Heidelberg (2004)
Früh, T., Kurth, W.: The hydraulic system of trees: Theoretical framework and numerical simulation. J. Theor. Biol. 201, 251–270 (1999)
Giavitto, J.L., Godin, C., Michel, O., Prusinkiewicz, P.: Computational Models for Integrative and Developmental Biology. In: Modelling and Simulation of Biological Processes in the Context of Genomics, Hermes (July 2002)
Gosling, J., Joy, B., Steele, G., Bracha, G.: The Java Language Specification, 3rd edn. Addison-Wesley, Amsterdam (June 2005)
Hemmerling, R., Kniemeyer, O., Lanwert, D., Kurth, W., Buck-Sorlin, G.: The rule-based language XL and the modelling environment GroIMP illustrated with simulated tree competition. Functional Plant Biology 35(9/10), 739–750 (2008)
Kniemeyer, O.: Design and Implementation of a Graph Grammar Based Language for Functional-Structural Plant Modelling. PhD thesis, University of Technology at Cottbus, Fakultät für Mathematik, Naturwissenschaften und Informatik (2008), http://opus.kobv.de/btu/volltexte/2009/593/
Kniemeyer, O., Barczik, G., Hemmerling, R., Kurth, W.: Relational Growth Grammars - a parallel graph transformation approach with applications in biology and architecture. In: Schürr, A., Nagl, M., Zündorf, A. (eds.) AGTIVE 2007. LNCS, vol. 5088, pp. 152–167. Springer, Heidelberg (2008)
Kniemeyer, O., Hemmerling, R., Kurth, W.: The XL Language Specification (2009), http://www.grogra.de/xlspec
Parter, S.: The use of linear graphs in Gauss elimination. SIAM Review 3(2), 119–130 (1961)
Press, W.H., Teukolsky, S.A., Vetterling, W.T., Flannery, B.P.: Numerical Recipes: The Art of Scientific Computing, 3rd edn. Cambridge University Press, New York (2007)
Prusinkiewicz, P., Allen, M., Escobar-Gutiérrez, A., DeJong, T.M.: Numerical methods for transport-resistance source-sink allocation models. In: Vos, J., Marcelis, L.F.M., de Visser, P.H.B., Struik, P.C., Evers, J.B. (eds.) Functional-Structural Plant Modelling in Crop Production, 1st edn. Wageningen UR Frontis Series, vol. 22, Springer, Heidelberg (2007)
Prusinkiewicz, P., Hammel, M.S., Mjolsness, E.: Animation of plant development. In: SIGGRAPH ’93: Proceedings of the 20th Annual Conference on Computer Graphics and Interactive Techniques, pp. 351–360. ACM, New York (1993)
Thornley, J.H.M., Johnson, I.R.: Plant and crop modelling: a mathematical approach to plant and crop physiology. Clarendon Press/Oxford University Press, Oxford/New York (1990)
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Hemmerling, R., Smoleňová, K., Kurth, W. (2010). A Programming Language Tailored to the Specification and Solution of Differential Equations Describing Processes on Networks. In: Dediu, AH., Fernau, H., Martín-Vide, C. (eds) Language and Automata Theory and Applications. LATA 2010. Lecture Notes in Computer Science, vol 6031. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-13089-2_25
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DOI: https://doi.org/10.1007/978-3-642-13089-2_25
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