Finite Difference Methods for ODE Boundary Value Problems

7.2. Finite Difference Methods for ODE Boundary Value Problems#

Version of December 8, 2025

References:

  • [Sauer, 2022] Section 7.2, Finite Difference Methods.

7.2.1. Introduction#

This is for now just a stub; the section will introduce finite difference methods for solving ODE BVPs in the form

\[ u'' + p(x) u' + q(x)u = f(x),\ a \leq x \leq b \]

with boundary conditions such as the Homogeneous Dirichlet Boundary conditions

\[ u(a) = u(b) = 0 \]

We will then also consider the related eigenvalue problem

\[ u'' + p(x) u' + q(x)u = \lambda u \]
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