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Discretization of nonlinear models by sinc collocation-interpolation methods. (English) Zbl 0858.65104
Summary: This paper deals with the solution of initial-boundary value problems for nonlinear evolution equations in one and two space dimensions. The solution technique is based on collocation-interpolation methods which use sinc functions. The paper aims to provide a guideline towards a large number of nonlinear problems of interest in applied sciences.

65M70 Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs
35K55 Nonlinear parabolic equations
Full Text: DOI
[1] Bellomo, N.; Preziosi, L., Modelling, mathematical methods and scientific computation, (1995), CRC Press Boca Raton, FL · Zbl 0871.65001
[2] Bellman, R.; Kashef, B.; Casti, J., Differential quadrature: solution of nonlinear partial differential equations, J. comp. phys., 10, 40-52, (1972) · Zbl 0247.65061
[3] Satofuka, A., A new explicit method for the solution of parabolic differential equations, (), 97-108
[4] Bellomo, N.; Brzezniak, Z.; de Socio, L.M., Nonlinear stochastic evolution problems in applied sciences, (1992), Kluwer Amsterdam · Zbl 0770.60061
[5] Stenger, F., Numerical methods based on wittaker cardinal or sinc functions, SIAM review, 23, 165-224, (1983) · Zbl 0461.65007
[6] Stenger, F., Numerical methods based on sinc and analytic functions, (1993), Springer Berlin · Zbl 0803.65141
[7] Lund, J.; Bowers, K., Sinc methods, (1992), SIAM Philadelphia, PA · Zbl 0753.65081
[8] Stenger, F., Book review: sinc methods by J. Lund and K. bowers, SIAM review, 33, 682-683, (1993)
[9] Sandberg, I., The reconstruction of band-limited signals from nonuniformly spaced samples, IEEE trans. circ. and systems, 41, 64-66, (1994) · Zbl 0846.94008
[10] Bellomo, N.; Ridolfi, L., Solution of nonlinear initial-boundary value problems by sinc collocation-interpolation methods, Computers math. applic., 29, 4, 15-28, (1995) · Zbl 0822.65075
[11] Preziosi, L.; Teppati, G.; Bellomo, N., Modeling and solution of stochastic inverse problems in mathematical physics, Mathl. comput. modelling, 16, 5, 37-51, (1992) · Zbl 0755.60102
[12] Nayfeh, A.H.; Nayfeh, S.A.; Pakdemirli, M., On the discretization of weakly nonlinear spatially continuous systems, (), 175-200 · Zbl 0855.73042
[13] ()
[14] ()
[15] Back, J.; Blackwell, B.; Clair, C.St., Inverse heat conduction, (1985), Wiley London
[16] Quarteroni, A., Domain decomposition methods using spectral methods, Surveys math. ind., 1, 75-115, (1991)
[17] Jager, E.; Segel, L., On the distribution of dominance in a population of interacting anonymous organisms, SIAM J. appl. math., 52, 1442-1468, (1992) · Zbl 0759.92011
[18] Arlotti, L.; Bellomo, N., On a new model of population dynamics with stochastic interaction, Transp. theory statist. phys., 24, 431-443, (1995) · Zbl 0838.92018
[19] L. Arlotti and N. Bellomo, On the Cauchy problem for an nonlinear integral equation in population dynamics, Appl. Math. Lett. (submitted). · Zbl 0853.35050
[20] Bellomo, N.; Forni, G., Dynamics of tumor interaction with the host immune system, Mathl. comput. modelling, 20, 1, 107-122, (1994) · Zbl 0811.92014
[21] Bellomo, N.; Preziosi, L.; Forni, G., Tumors immune system interactions: the kinetic cellular theory, ()
[22] Arlotti, L.; Lachowicz, M., Qualitative analysis of a nonlinear integro differential equation modelling tumor host dynamics, (), 11-29 · Zbl 0859.92011
[23] Smoluchowski, M., Versuch einer mathematischen theorie der koagulationskinetik, Z. phys. chem., 92, 129-168, (1917)
[24] Longo, E.; Preziosi, L.; Bellomo, N., The semicontinuous Boltzmann equation: towards a model for fluid dynamic applications, Math. models and methods in appl. sci., 3, 65-93, (1993) · Zbl 0770.76057
[25] White, W., A global existence theorem for Smoluchowski’s equation, (), 273-276 · Zbl 0442.34003
[26] Kreer, M.; Penrose, O., Proof of dynamical scaling in Smoluchowski’s coagulation equation with constant kernel, J. statist. phys., 75, 389-407, (1994) · Zbl 0828.60093
[27] Cercignani, C., Theory and application of the Boltzmann equation, (1988), Springer Berlin
[28] Daubechies, I., Ten lectures on wavelets, (1992), SIAM Philadelphia, PA · Zbl 0776.42018
[29] Zeider, E., Applied functional analysis, (1995), Springer Berlin
[30] Schmidt, G., On spline collocation methods for boundary integral equations in the plane, Math. methods in appl. sci., 7, 74-89, (1985) · Zbl 0577.65107
[31] Bellomo, N.; Flandoli, F., Stochastic partial differential equations in continuum physics, Mathl. comp. in simul., 31, 3-17, (1988) · Zbl 0706.60063
[32] Temam, R., Numerical analysis, (1973), Reidel Dordrecht
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