Stability and Multiplicity of Solutions to Discretizations of Nonlinear Ordinary Differential Equations

Beyn W-J, Doedel E (1981)
SIAM Journal on Scientific and Statistical Computing 2(1): 107-120.

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A large class of consistent and unconditionally stable discretizations of nonlinear boundary value problems is defined. The number of solutions to the discretizations is compared to the number of solutions of the continuous problem. We state conditions under which these numbers must agree for all sufficiently small mesh sizes. Various examples, including bifurcation problems, illustrate our theoretical results.
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Beyn W-J, Doedel E. Stability and Multiplicity of Solutions to Discretizations of Nonlinear Ordinary Differential Equations. SIAM Journal on Scientific and Statistical Computing. 1981;2(1):107-120.
Beyn, W. - J., & Doedel, E. (1981). Stability and Multiplicity of Solutions to Discretizations of Nonlinear Ordinary Differential Equations. SIAM Journal on Scientific and Statistical Computing, 2(1), 107-120.
Beyn, W. - J., and Doedel, E. (1981). Stability and Multiplicity of Solutions to Discretizations of Nonlinear Ordinary Differential Equations. SIAM Journal on Scientific and Statistical Computing 2, 107-120.
Beyn, W.-J., & Doedel, E., 1981. Stability and Multiplicity of Solutions to Discretizations of Nonlinear Ordinary Differential Equations. SIAM Journal on Scientific and Statistical Computing, 2(1), p 107-120.
W.-J. Beyn and E. Doedel, “Stability and Multiplicity of Solutions to Discretizations of Nonlinear Ordinary Differential Equations”, SIAM Journal on Scientific and Statistical Computing, vol. 2, 1981, pp. 107-120.
Beyn, W.-J., Doedel, E.: Stability and Multiplicity of Solutions to Discretizations of Nonlinear Ordinary Differential Equations. SIAM Journal on Scientific and Statistical Computing. 2, 107-120 (1981).
Beyn, Wolf-Jürgen, and Doedel, Eusebius. “Stability and Multiplicity of Solutions to Discretizations of Nonlinear Ordinary Differential Equations”. SIAM Journal on Scientific and Statistical Computing 2.1 (1981): 107-120.
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