2 examples of the method of characteristics for solving PDEs
1. Use the method of characteristics to solve the advection equation du/dt=-kdu/dx-ru subject to the initial condition u(x,0)=f(x). 2. Use the method of characteristics to solve du/dt+te^(-t^2))du/dx=usin(t) subject to the initial condition u(x,0)=e^(-x^2)) (See attachment for the above questions formatt ...continues
Solving the wave equation using separation of variables
See the attachment for the questions.
A solution of the 2d Laplace equation using separation of variables.
Solve Laplace of u = 0 subject to the conditions:
u(x,0) = f1(x)
u(0,y) = 0
u(x,b) = 0
u(a,y) = 0
0
Fourier Series and Boundary Value Problems
Please help with the following problems : # 4, # 6 and # 8.
1. Consider the first order PDE, ∂u/∂t = ct(∂u/∂x) -∞ < x < ∞ c does not equal 0 a) Find the fundamental solution b) Use the fundamental solution and convolution to find a formula for the solution to: ∂u/∂t = ct(∂u/∂x) -∞ < x < ∞ ...continues
PDE - The convolution of two functions
See attached problem (convolution of two functions)
Nature of a turning point of a function of 2 variables
Could you please do the problem attached? Thank you.
Find general solutions for the attached differential equations.
I'm having trouble with a PDE problem, I've indicated in the attached file what specifically.
Please see the attachment for full description.