References
Carnevale N, Hines M (2006) The NEURON book. Cambridge University Press, Cambridge, UK
Crank J, Nicholson P (1947) A practical method for numerical evaluation of solutions of partial differential equations of the heat-conduction type. Proc Camb Philos Soc 43:50–67
Golowasch J, Goldman M, Abbott L, Marder E (2002) Failure of averaging in the construction of a conductance-based neuron model. J Neurophysiol 87:1129–1131
Hindmarsh AC, Brown PN, Grant KE, Lee SL, Serban R, Shumaker DE, Woodward CS (2005) SUNDIALS: suite of nonlinear and differential/algebraic equation solvers. ACM Trans Math Softw (TOMS) 31:363–396
Hines M (1984) Efficient computation of branched nerve equations. international Journal of Bio-Medical Computation 15:69–76
Hines M, Carnevale N (2001) NEURON: a tool for neuroscientists. Neuroscientist 7:123–135
Hodgkin A, Huxley A (1952) A quantitative description of membrane current and its application to conduction and excitation in nerve. J Physiol 117:500–544
Iserles A (2008) A first course in the numerical analysis of differential equations. Cambridge University Press, Cambridge, UK
Jack J, Noble D, Tsien R (1983) Electric current flow in excitable cells. Oxford University Press, London
Numerical solution of partial differential equations. (2013). In: Wolfram Mathematica Virtual Book. http://reference.wolfram.com/mathematica/tutorial/NDSolvePDE.html
Polyanin AD, Schiesser WE, Zhurov AI (2008) Partial differential equation. Scholarpedia 3:4605
Rall W (1977) Core conductor theory and cable properties of neurons. In: Kandel ER (ed) Handbook of physiology, vol 1, Part I: the nervous system. American Physiological Society, Bethesda, pp 39–98
Segev I, Rinzel J, Shepherd G (eds) (1995) The theoretical foundation of dendritic function: collected papers of wilfrid rall with commentaries. MIT Press, Cambridge, MA
Zador A, Koch C (1994) Linearized models of calcium dynamics – formal equivalence to the cable equation. J Neurosci 14:4705–4715
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Hines, M., Carnevale, T. (2014). Numerical Integration Methods. In: Jaeger, D., Jung, R. (eds) Encyclopedia of Computational Neuroscience. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-7320-6_242-1
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