Numerical Analysis of Boundary-Value Problems for Singularly-Perturbed Differential-Difference Equations with Small Shifts of Mixed Type

M.K. Kadalbajoo and K.K. Sharma
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M.K. Kadalbajoo: Indian Institute of Technology
K.K. Sharma: Indian Institute of Technology

Journal of Optimization Theory and Applications, 2002, vol. 115, issue 1, No 9, 145-163

Abstract: Abstract In this paper, we use a numerical method to solve boundary-value problems for a singularly-perturbed differential-difference equation of mixed type, i.e., containing both terms having a negative shift and terms having a positive shift. Similar boundary-value problems are associated with expected first exit time problems of the membrane potential in models for the neuron. The stability and convergence analysis of the method is given. The effect of a small shift on the boundary-layer solution is shown via numerical experiments. The numerical results for several test examples demonstrate the efficiency of the method.

Keywords: Singular perturbations; differential-difference equations; boundary layers; negative shifts; positive shifts; action potential (search for similar items in EconPapers)
Date: 2002
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Citations: View citations in EconPapers (5)

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DOI: 10.1023/A:1019681130824

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