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Weak Formulation in Boundary Value Problems

Learn about the weak formulation in BVPs through the application of Green’s theorem and Green’s first identity in R^2. Explore the Dirac delta function properties and its representation as a generalized function with sharp peaks.

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Weak Formulation in Boundary Value Problems

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  1. Weak Formulation BVP Weak Formulation ( variational formulation) Multiply equation (1) by and then integrate over the domain Green’s theorem gives where

  2. Green’s First identity in R^2 (p285) Green’s First Identity

  3. Dirac delta function Dirac delta function

  4. Dirac delta function Dirac delta function

  5. Dirac delta function Dirac delta function it is a generalized function representing an infinitely sharp peak bounding unit area: a 'function' δ(x) that has the value zero everywhere except at x = 0 where its value is infinitely large

  6. Dirac delta function Properties

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