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Numerical Analysis of Boundary Layer Problems (Classic Reprint) - Hardcover

William D. Murphy

 
9780332149035: Numerical Analysis of Boundary Layer Problems (Classic Reprint)

Synopsis

Learn how careful finite difference methods can reliably solve boundary layer problems and prevent divergence.

Boundary layer analysis and numerical methods are explored with a focus on stability, consistency, and convergence. The discussion explains how difference equations approximate ODEs and what conditions ensure the computed solution remains faithful as the mesh is refined. You’ll see how classic results, such as the Dahlquist stability theory, guide the design of effective schemes for challenging boundary layer problems.

  • Understand the roles of consistency and stability in finite difference schemes
  • See how convergence is connected to the behavior of polynomial roots and the unit circle
  • Learn what makes certain methods perform well inside the boundary layer and why others fail
  • Get practical guidance on selecting and evaluating numerical schemes for boundary layer equations
Ideal for readers seeking a practical foundation in numerical analysis of boundary layer problems and the design of stable, convergent difference methods.

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