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Forward-Backward Differential Equations: Approximation of Small Solutions

M. Filomena Teodoro,Pedro M. Lima,Neville J. Ford,Patricia M. Lumb-2013-01-01-Portuguese National Funding Agency for Science, Research and Technology (RCAAP Project by FCT)
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TL;DRAbstract

In the context of physics, economic dynamics, nance, optimal control, biology and other applied sciences, many mathematical models contain mixed type functional differential equations (MTFDEs), equations with both delayed and advanced arguments. Knowing from the analysis of delay di erential equations (DDEs) that the evaluation of small solutions (that decay faster than any exponential) often leads to computational problems (degeneracy), we investigate this subject in the case of MTFDEs. Some computations have been carried out and are presented here, concerning the linear nonautonomous case. We continue this work and extend the investigation to other problems.

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In the context of physics, economic dynamics, nance, optimal control, biology and other applied sciences, many mathematical models contain mixed type functional differential equations (MTFDEs), equations with both delayed and advanced arguments. Knowing from the analysis of delay di erential equations (DDEs) that the evaluation of small solutions (that decay faster than any exponential) often leads to computational problems (degeneracy), we investigate this subject in the case of MTFDEs. Some computations have been carried out and are presented here, concerning the linear nonautonomous case. We continue this work and extend the investigation to other problems.

Keywords

Context (archaeology)MathematicsDifferential equationApplied mathematicsDelay differential equationDegeneracy (biology)Exponential functionComputation

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