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Part BCSIR NET June 2023greens-function-dirichlet

Greens function dirichlet

For the unknown , consider the boundary value problem y″(x) + 2y(x) = 0 for x ∈ (0,1), y(0) = y(1) = 0. It is given that it corresponds to the integral equation dt. Which of the following is the kernel K(x, t)?

  1. A.K(x,t) = t(1 − x) for t < x; x(1 − t) for t > x✓
  2. B. for for t > x
  3. C. for for t > x
  4. D. for for t > x

Solution

The Green's function of −y″ with Dirichlet conditions on [0,1] is G(x,t) = t(1 − x) for t < x and x(1 − t) for t > x; then .

The trap it tests

Execution slip

The idea was right. The computation was not.

Drill statements like this

Related counterexample: Every integral equation of the second kind has a unique solution

More on this topic

From Linear Integral Equations › Fredholm and Volterra equations

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