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Solution of the partial differential equation of the Hodgkin-Huxley model using differential quadrature. (English) Zbl 0273.65088

MSC:
65N35 Spectral, collocation and related methods for boundary value problems involving PDEs
92B05 General biology and biomathematics
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[1] Hodgkin, A.L.; Huxley, A.F., A quantitative description of membrane current and its application to conduction and excitation in nerve, J. physiol., 117, (1952)
[2] Cooley, J.W.; Dodge, F.A., Digital computer solutions for excitation and propagation of the nerve impulse, Biophys. J., 6, (1966)
[3] Fitz Hugh, R.; Antosiewicz, H.A., Automatic computation of nerve excitation, detailed corrections and additions, J. SIAM, 7, (1959) · Zbl 0089.15703
[4] Bellman, R.; Kashef, B.G.; Casti, J., Differential quadrature: a technique for the rapid solution of nonlinear partial differential equations, J. of comp. phys., 10, (1972) · Zbl 0247.65061
[5] R. Bellman, B. Kashef, and R. Vasudevan, Differential quadrature, partial differential equations and splines, unpublished. · Zbl 0335.65023
[6] Greville, T.N.E., Theory and applications of spline functions, (1969), Academic New York · Zbl 0215.17601
[7] Bellman, R.; Kashef, B.G.; Vasudevan, R., Splines via dynamic programming, J. of math. anal. and appl., (1972) · Zbl 0241.41006
[8] Leiberstein, H.M., On the Hodgkin-Huxley partial differential equation, Math. biosci., 1, (1967)
[9] Kaplan, S.; Trujillo, D., Numerical studies of the partial differential equations governing nerve impulse conduction, Math. biosci., 7, (1970) · Zbl 0197.16602
[10] Bellman, R.; Kashef, B., Application of splines and differential quadrature to partial differential equation of Hodgkin-Huxley type, Proceedings of the fifth hawaii international conference on system sciences supplement, 199, (1972)
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