6) Solution of PDEs by Separation of Variables Flashcards
1
Q
What defines a PDE having homogenous boundary conditions
A
Homogenous Boundary Conditions:
g0 (t) = 0 and g1(t) = 0
2
Q
What are the key steps in applying separation of variables to solve homogeneous PDEs
A
3
Q
How do you solve the eigenvalue problem X′′ (x) - λX(x) = 0
A
4
Q
What is the Superposition Theorem in the context of linear homogeneous PDEs
A
5
Q
How do Fourier series help in managing initial conditions when solving PDEs
A
6
Q
How do the solutions for X(x) and Y(y) in a separable ODE vary with different values of the separation constant λ
A
7
Q
How do you solve inhomogeneous PDEs using separation of variables
A
8
Q
How do you solve Laplace’s Equation in a disk using polar coordinate
A
9
Q
How do you solve a PDE with variables x, y, and t using separation of variables
A
