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Secant versus tangent methods in non-linear heat transfer analysis. (English) Zbl 0441.65089


MSC:

65Z05 Applications to the sciences
35K60 Nonlinear initial, boundary and initial-boundary value problems for linear parabolic equations
65N22 Numerical solution of discretized equations for boundary value problems involving PDEs
65H10 Numerical computation of solutions to systems of equations
80A20 Heat and mass transfer, heat flow (MSC2010)
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References:

[1] ’Evaluating time integration methods for nonlinear dynamics analysis’ in Finite Element Analysis of Transient Nonlinear Structural Behavior, ASME Appl. Mech. Symp. Series, AMD-14, 35-58, 1975.
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[3] and , ’Direct time integration methods in non-linear structural mechanics’, FENOMECH 78, ISD, Univ. Stuttgart, Stuttgart, RFA, September 1978.
[4] and , ’Nonlinear heat transfer by finite element tangent conductivity methods’ in Finite Elements in Nonlinear Mechanics, Ed. Trondheim, Norway, Vol. 2, 767-785, 1978.
[5] and , ’On some implicit one-step methods for stiff differential equations’, KTH Report TRITA-NA-7302, Stockholm, 1973.
[6] ’Stability of one-step methods in transient nonlinear heat conduction’, Paper B2/10, Proc. Int. Conf. SMIRT-4, San Francisco, 1977.
[7] ’Accuracy and cost of integration techniques for nonlinear heat transfer’ in Finite Elements in the Commercial Environment, Ed. Bournemouth, UK, Vol. 1, 133-154, 1978.
[8] Hogge, Comp. Meth. Appl. Mech. Eng. 11 pp 281– (1977)
[9] Wilson, Nucl. Eng. Design 29 pp 110– (1974)
[10] and , ’Analysis of nonlinear heat transfer and field problems’, Applications using ADINA, MIT Report 82448-6, Cambridge, 230-262, 1977.
[11] et al., ’A stable computational scheme for stiff time-dependent constitutive equations’, Paper L2/2, Proc. Int. Conf. SMIRT-4, San Fransisco, 1977.
[12] Hogge, Appl. Math. Modelling 1 pp 319– (1977)
[13] Lardner, AIAA J. 1 pp 196– (1963)
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