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Sensitivity computations in higher order continuation methods. (English) Zbl 1452.35087

Summary: Sensitivity analysis is a key tool in the study of the relationships between the input parameters of a model and the output solution. Although sensitivity analysis is extensively addressed in the literature, little attention has been brought to the methodological aspects of the sensitivity of nonlinear parametric solutions computed through a continuation technique. This paper proposes four combinations of sensitivity analysis with continuation and homotopy methods, including sensitivity analysis along solution branches or at a particular point. Theoretical aspects are discussed in the higher order continuation framework Diamant. The sensitivity methods are applied to a thermal ignition problem and some free vibration problems. Remarkable eigenvalue maps are produced for the complex nonlinear eigenvalue problems.

MSC:

35K91 Semilinear parabolic equations with Laplacian, bi-Laplacian or poly-Laplacian
35K20 Initial-boundary value problems for second-order parabolic equations
65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs
65P30 Numerical bifurcation problems
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