Skip to main content

The Analytical Behaviour of Solutions

  • 942 Accesses

Part of the Lecture Notes in Mathematics book series (LNM,volume 1985)

Abstract

In this chapter, we gather a number of analytical properties for singularly perturbed boundary-value problems for second-order ordinary differential equations of the general type

$$ - \in u^ - bu^{'} + cu = f\text{ in }(0,1),u(0) = \gamma _0 ,\text{ }u(1) = \gamma _1 ,$$

with a small positive parameter ε and functions b, c, f : [0, 1] → IR, and of its vector-valued counterpart

$$ - Eu^ - Bu^{'} + Au = f\text{ in }(0,1),u(0) = \gamma _0 ,\text{ }u(1) = \gamma _1 ,$$

with \( E = \text{diag}(\in ),\in = (\in _1 ,....,\in _\ell )^T \) and small positive constants \(\in _i ,i = 1,...,\ell ,\) with matrix-valued functions A, B : \( [0,1] \to IR^{\ell ,\ell } ,\), and vector-valued functions \( f,u:[0,1] \to IR^\ell \).

Keywords

  • Differential Operator
  • Analytical Behaviour
  • Comparison Principle
  • Coupling Matrix
  • Solution Decomposition

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

This is a preview of subscription content, access via your institution.

Buying options

Chapter
USD   29.95
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   39.99
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   54.99
Price excludes VAT (Canada)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Torsten Linß .

Rights and permissions

Reprints and Permissions

Copyright information

© 2010 Springer-Verlag Berlin Heidelberg

About this chapter

Cite this chapter

Linß, T. (2010). The Analytical Behaviour of Solutions. In: Layer-Adapted Meshes for Reaction-Convection-Diffusion Problems. Lecture Notes in Mathematics(), vol 1985. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-05134-0_3

Download citation