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Dissipativity of \(\theta \)-methods for a class of nonlinear neutral delay differential equations. (English) Zbl 1155.65059

The paper is concerned with the property of dissipativity of neutral delay differential equations when solved using \(\theta\)-methods. The paper is structured as follows: After an initial introduction providing background to dissipativity, the authors provide results, respectively, on dissipativity for neutral delay differential equations, dissipativity for linear \(\theta\)-methods and dissipativity for one leg \(\theta\)-methods.

MSC:

65L05 Numerical methods for initial value problems involving ordinary differential equations
34K28 Numerical approximation of solutions of functional-differential equations (MSC2010)
34K40 Neutral functional-differential equations
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References:

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