7: Green's Functions and Nonhomogeneous Problems
- Page ID
- 90267
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- 7.1: Initial Value Green’s Functions
- In this section we will investigate the solution of initial value problems involving nonhomogeneous differential equations using Green’s functions.
- 7.2: Boundary Value Green’s Functions
- In this section we will extend this method to the solution of nonhomogeneous boundary value problems using a boundary value Green’s function.
- 7.3: The Nonhomogeneous Heat Equation
- Boundary value green’s functions do not only arise in the solution of nonhomogeneous ordinary differential equations. They are also important in arriving at the solution of nonhomogeneous partial differential equations. In this section we will show that this is the case by turning to the nonhomogeneous heat equation.
- 7.4: Green’s Functions for 1D Partial Differential Equations
- Here we can introduce Green’s functions of different types to handle nonhomogeneous terms, nonhomogeneous boundary conditions, or nonhomogeneous initial conditions. Occasionally, we will stop and rearrange the solutions of different problems and recast the solution and identify the Green’s function for the problem.
- 7.5: Green’s Functions for the 2D Poisson Equation
- In this section we consider the two dimensional Poisson equation with Dirichlet boundary conditions.
- 7.6: Method of Eigenfunction Expansions
- We have seen that the use of eigenfunction expansions is another technique for finding solutions of differential equations. In this section we will show how we can use eigenfunction expansions to find the solutions to nonhomogeneous partial differential equations. In particular, we will apply this technique to solving nonhomogeneous versions of the heat and wave equations.