Homework Answers
Add Answer to:
1. Wave equation. Consider the wave equation on the finite interval (0, L) PDE BC where Neumann b...
Objective: Solve the wave equation numerically using finite difference methods with both dirichle...
Need help solving it using matlab with for loop
Objective: Solve the wave equation numerically using finite difference methods with both dirichlet and neumann conditions. Consider the wave equation for a string with fixed ends, L=1. lu lu Initial conditions. To make the string behave like a plucked guitar string, use a triangual initial condition. For x less than or equal to 0.5, set u(x, t 0) = 2HX and for x greater than 0.5, use u(x, t = 0)...
We can expect the solution u(x,y) to be in the form X(x)Y(y). or I believe that...
We can expect the solution u(x,y) to be in the form
X(x)Y(y).
or
I believe that these are the correct forms of X(x) and Y(y).
2. Laplace's equation Consider Laplace's equation on the rectangle with 0 < x < L and 0 < < H: PDE BC BC BC u(x,0) 0, u(z, H) = g(z). (10) where a mixture of Dirichlet and Neumann boundary conditions is specified, and only one of the sides has a boundary condition that is nonhomogeneous...
Consider the following second order PDE Uit – 9Uxx = 0, 0<x< < t > 0,...
Consider the following second order PDE Uit – 9Uxx = 0, 0<x< < t > 0, (A) and the following boundary value/initial conditions: Ux(t,0) = uſt, 5) = 0, t>0, u(0, x) = 44(0, x) = 4 cos’ x, 0<x< (BC) (IC) for the function u= u(t, x). a. (5 points) Find ordinary differential equations for functions T = T(t) and X = X(x) such that the function u(t, x) = T(t)X(x) satisfies the PDE (A). b. (5 points) Find...
14 points Consider the following equation : PDE: u+ 0 ,0<x <1, 0<y <1 BCs: u(0, y)= 0, u (1, y ) = 0 ,0...
14 points Consider the following equation : PDE: u+ 0 ,0<x <1, 0<y <1 BCs: u(0, y)= 0, u (1, y ) = 0 ,0<y <1 ICs: u (x,0)=0, u (x,1)=2 ,0<x <1 a) Using the PDE and the boundary conditions write the form of the solution u (x ,t) b) Now apply the initial condition to solve for the unknown coefficients in the solution from part (a)
14 points Consider the following equation : PDE: u+ 0 ,0
b) Consider the wave equation azu azu at2 0 < x < 2, t>0, ar2 with...
b) Consider the wave equation azu azu at2 0 < x < 2, t>0, ar2 with boundary conditions u(0,t) = 0, u(2, t) = 0, t> 0, and initial conditions u(x,0) = x(2 – x), ut(x,0) = = 0, 0 < x < 2. Use the method of separation of variables to determine the general solution of this equation. (15 marks)
3. Consider the non homogeneous heat equation ut- urr+ 1 with non homogeneous boundary conditions u(0. t) 1, u(1t) (a) Find the equilibrium solution ueqx) to the non homogeneous equation. (b) The sol...
3. Consider the non homogeneous heat equation ut- urr+ 1 with non homogeneous boundary conditions u(0. t) 1, u(1t) (a) Find the equilibrium solution ueqx) to the non homogeneous equation. (b) The solution w(r, t) to the homogenized PDE wt-Wra, with w(0,t,t)0 1S -1 Verify that ugen(x, t)Ue(x) +w(x, t) solves the full PDE and BCs (c) Let u(x,0)- f(x) - 2 - ^2 be the initial condition. Find the particular solution by specifying all Fourier coefficients
3. Consider the...
2. In lectures we solved the heat PDE in 1 +1 dimensions with constant-temperature boundary conditions u(0,t)u(L,t) -0. If these boundary conditions change from zero temperature, we need to do a litt...
2. In lectures we solved the heat PDE in 1 +1 dimensions with constant-temperature boundary conditions u(0,t)u(L,t) -0. If these boundary conditions change from zero temperature, we need to do a little bit more work. Consider the following initial/boundary-value problem (IBVP) 2 (PDE) (BCs) (IC) u(0,t) = a, u(x,00, u(L, t)=b, st. and let's take L = 1, a = 1, b = 2 throughout for simplicity. Solve this problem using the following tricks b and A"(x)-0 (a) Find a...
This is PDE problem. Please show all steps in detail with neat handwriting. Problem . Consider...
This is PDE problem. Please show all steps in detail with neat
handwriting.
Problem . Consider the function a) Find the full Fourier Series of F(x) a(0, y, t) = u(a, y, t) 0 u(z, 0, t ) = u(z, b, l) = 0 u(z,y,0) = f(z,y), u(x, y,0)-g(x,y), 0<y< b,t0 a) b) Solve the initial-boundary value problem for 2D wave equation. What is the physical interpretation of these boundary conditions
1. Consider the insulated heat equation up = cum, 0 <r<L, t > 0 u (0,t)...
1. Consider the insulated heat equation up = cum, 0 <r<L, t > 0 u (0,t) = u (L, t) = 0, t > 0 u(x,0) = f(2). What is the steady-state solution? 2. Solve the two-dimensional wave equation (with c=1/) on the unit square (i.e., [0, 1] x [0,1) with homogeneous Dirichlet boundary conditions and initial conditions: (2, y,0) = sin(x) sin(y) (,y,0) = sin(x). 3. Solve the following PDE: Uzr + Uyy = 0, 0<<1,0 <y < 2...
= 0 over the domains 0<x<1 and t>0, where x is space and t is time...
= 0 over the domains 0<x<1 and t>0, where x is space and t is time at ax ди (1,1) = 0 ax Dirichlet and Neumann BCs are u(0, t)=80; Find the solution of the PDE that satisfies the given IC and BCs a. IC: u(x,0) 25sin (nx)
Need help solving it using matlab with for loop
Objective: Solve the wave equation numerically using finite difference methods with both dirichlet and neumann conditions. Consider the wave equation for a string with fixed ends, L=1. lu lu Initial conditions. To make the string behave like a plucked guitar string, use a triangual initial condition. For x less than or equal to 0.5, set u(x, t 0) = 2HX and for x greater than 0.5, use u(x, t = 0)...
We can expect the solution u(x,y) to be in the form
X(x)Y(y).
or
I believe that these are the correct forms of X(x) and Y(y).
2. Laplace's equation Consider Laplace's equation on the rectangle with 0 < x < L and 0 < < H: PDE BC BC BC u(x,0) 0, u(z, H) = g(z). (10) where a mixture of Dirichlet and Neumann boundary conditions is specified, and only one of the sides has a boundary condition that is nonhomogeneous...
Consider the following second order PDE Uit – 9Uxx = 0, 0<x< < t > 0, (A) and the following boundary value/initial conditions: Ux(t,0) = uſt, 5) = 0, t>0, u(0, x) = 44(0, x) = 4 cos’ x, 0<x< (BC) (IC) for the function u= u(t, x). a. (5 points) Find ordinary differential equations for functions T = T(t) and X = X(x) such that the function u(t, x) = T(t)X(x) satisfies the PDE (A). b. (5 points) Find...
14 points Consider the following equation : PDE: u+ 0 ,0<x <1, 0<y <1 BCs: u(0, y)= 0, u (1, y ) = 0 ,0<y <1 ICs: u (x,0)=0, u (x,1)=2 ,0<x <1 a) Using the PDE and the boundary conditions write the form of the solution u (x ,t) b) Now apply the initial condition to solve for the unknown coefficients in the solution from part (a)
14 points Consider the following equation : PDE: u+ 0 ,0
b) Consider the wave equation azu azu at2 0 < x < 2, t>0, ar2 with boundary conditions u(0,t) = 0, u(2, t) = 0, t> 0, and initial conditions u(x,0) = x(2 – x), ut(x,0) = = 0, 0 < x < 2. Use the method of separation of variables to determine the general solution of this equation. (15 marks)
3. Consider the non homogeneous heat equation ut- urr+ 1 with non homogeneous boundary conditions u(0. t) 1, u(1t) (a) Find the equilibrium solution ueqx) to the non homogeneous equation. (b) The solution w(r, t) to the homogenized PDE wt-Wra, with w(0,t,t)0 1S -1 Verify that ugen(x, t)Ue(x) +w(x, t) solves the full PDE and BCs (c) Let u(x,0)- f(x) - 2 - ^2 be the initial condition. Find the particular solution by specifying all Fourier coefficients
3. Consider the...
2. In lectures we solved the heat PDE in 1 +1 dimensions with constant-temperature boundary conditions u(0,t)u(L,t) -0. If these boundary conditions change from zero temperature, we need to do a little bit more work. Consider the following initial/boundary-value problem (IBVP) 2 (PDE) (BCs) (IC) u(0,t) = a, u(x,00, u(L, t)=b, st. and let's take L = 1, a = 1, b = 2 throughout for simplicity. Solve this problem using the following tricks b and A"(x)-0 (a) Find a...
This is PDE problem. Please show all steps in detail with neat
handwriting.
Problem . Consider the function a) Find the full Fourier Series of F(x) a(0, y, t) = u(a, y, t) 0 u(z, 0, t ) = u(z, b, l) = 0 u(z,y,0) = f(z,y), u(x, y,0)-g(x,y), 0<y< b,t0 a) b) Solve the initial-boundary value problem for 2D wave equation. What is the physical interpretation of these boundary conditions
1. Consider the insulated heat equation up = cum, 0 <r<L, t > 0 u (0,t) = u (L, t) = 0, t > 0 u(x,0) = f(2). What is the steady-state solution? 2. Solve the two-dimensional wave equation (with c=1/) on the unit square (i.e., [0, 1] x [0,1) with homogeneous Dirichlet boundary conditions and initial conditions: (2, y,0) = sin(x) sin(y) (,y,0) = sin(x). 3. Solve the following PDE: Uzr + Uyy = 0, 0<<1,0 <y < 2...
= 0 over the domains 0<x<1 and t>0, where x is space and t is time at ax ди (1,1) = 0 ax Dirichlet and Neumann BCs are u(0, t)=80; Find the solution of the PDE that satisfies the given IC and BCs a. IC: u(x,0) 25sin (nx)
Most questions answered within 3 hours.
-
Briefly describe:
Investigating and assessing the impact of cost management
quality (CMQ) on the:
(a) effectiveness...
asked 1 hour ago -
Part A:
Use Henry's law to determine the molar solubility of helium at a
pressure of...
asked 2 hours ago -
Can you store the following chemicals in the same storage area:
yes, no and why
a....
asked 4 hours ago -
Hello class,
I found this article to be very interesting and relevant to the
concepts we...
asked 4 hours ago -
Consider the following relational database schema, which
describes the schedule of competition among National Football
(soccer)...
asked 6 hours ago -
Use the answer choices below for the next ____
questions
A) The Heart B) Veins C)...
asked 6 hours ago -
(Java) HELP!
Create a program that will ask the user to enter their first
name and...
asked 6 hours ago -
Suppose that the weight of an newborn fawn is Uniformly
distributed between 2.5 and 4 kg....
asked 6 hours ago -
Java Programming:
Make a Java program with two processes, a producer and a
consumer. If you...
asked 6 hours ago -
A pressure as low as 1 ✕ 10-8 torr can be achieved
using an oil diffusion...
asked 6 hours ago -
Identify the 6 major steps in an operational analysis
and briefly describe what each step is...
asked 6 hours ago -
The nucleus of the atom is composed of subatomic particles, one
of them being the proton...
asked 6 hours ago