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Differential quadrature and partial differential equations: Some numerical results. (English) Zbl 0521.65089


MSC:

65Z05 Applications to the sciences
65N22 Numerical solution of discretized equations for boundary value problems involving PDEs
80A32 Chemically reacting flows
35Q99 Partial differential equations of mathematical physics and other areas of application
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[1] Lee, E. S., Quasilinearization and Invariant Imbedding (1968), Academic Press: Academic Press New York · Zbl 0212.17602
[2] Bellman, R.; Kashef, B. G.; Casti, J., Differential quadrature: A technique for the rapid solution of nonlinear partial differential equations, J. Comput. Phys., 40-52 (1972) · Zbl 0247.65061
[3] Mingle, J. O., Computational considerations in nonlinear diffusion, Internat. J. Numer. Methods Engrg, 7, 103-116 (1973) · Zbl 0263.65102
[4] Kashef, B.; Bellman, R., Solution of the partial differential equation of the Hodgkin-Huxley model using differential quadrature, Math. Biosci., 19, 1-8 (1974) · Zbl 0273.65088
[5] Bellman, R., The inverse problem of estimating heart parameters from cardiograms, Math. Biosci., 19, 221-230 (1974) · Zbl 0276.92011
[6] Hu, L. C.; Hu, C.-R, Identification of rate constants by differential quadrature in partly measurable compartmental models, Math. Biosci., 21, 71-76 (1974) · Zbl 0305.93051
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[8] Bellman, R.; Kashef, B.; Lee, E. S.; Vasudevan, R., Differential quadrature and splines, Comput. Math. Appl., 1, 371-376 (1975) · Zbl 0335.65023
[9] Patton, R. J.; Linkens, D. A.; Dekker, L., A differential quadrature method for the simulation of gastro-intestinal electrical signals, (Proceedings of the Eighth AICA Congress on Simulation of Systems. Proceedings of the Eighth AICA Congress on Simulation of Systems, Delft, Netherlands, August 23-28, 1976 (1977), North-Holland: North-Holland Amsterdam), 641-647
[10] Mingle, J. O., The method of differential quadrature for transient nonlinear diffusion, J. Math. Anal. Appl., 60, 559-569 (1977) · Zbl 0372.65049
[11] Patton, R. J.; Linkens, D. A.; Banks, S. P.; Pritchard, A. J., Phenomenological investigation of a distributed parameter model for coordinating the mechanical activity of the mammalian Gut, (Control of Distributed Parameter Systems, Coventry, England, June 28-July 1, 1977 (1978), Pergamon: Pergamon Oxford), 493-509
[12] Bellman, R. E.; Roth, R. S., A scanning technique for systems identification, J. Math. Anal. Appl., 71, 403-411 (1979) · Zbl 0419.93023
[13] Liu, S. L.; Amundson, N. R., Stability of adiabatic packed bed reactors, Indust. Engrg. Chem. Fund., 2, 183 (1963)
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