Homework Answers
In this solution some basic concepts and formulas of Numerics are used. For more information, refer to any standard textbook or drop a comment below. Please give a Thumbs Up, if solution is helpful.
Solution :
NOTE : Feel free to ask further queries. Your positive rating would be appreciated and motivate me !
Add Answer to:
3. Determine the discretization of the heat equation driven at the boundary, PDE IC (x,0) BC t E R+ u(0, r) =g(x),ur(1,1) = 0, 3. Determine the discretization of the heat equation driven at the...
1. Wave equation. Consider the wave equation on the finite interval (0, L) PDE BC where Neumann b...
1. Wave equation. Consider the wave equation on the finite interval (0, L) PDE BC where Neumann boundary conditions are specified Physically, with Neumann boundary conditions, u(r, t) could represent the height of a fluid that sloshes between two walls. (a) Find the general Fourier series solution by repeating the derivation from class now considering Neumann instead of Dirichlet boundary conditions. Your final solution should be (b) Consider the following general initial conditions u(x, 0)x) IC IC Derive formulas that...
1. Solve the vibrating string problem PDE BC BC IC IC utt T.T Uz(0,t) = 0...
1. Solve the vibrating string problem PDE BC BC IC IC utt T.T Uz(0,t) = 0 u(1,t0 u(x,0cos(3T) 14(2.0) = x
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...
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...
=T 20 marks) Consider the following PDE with boundary and initial conditions: U = Upx +...
=T 20 marks) Consider the following PDE with boundary and initial conditions: U = Upx + ur, for 0<x< 1 and to with u(0,t) = 1, u(1,t) = 0, u(1,0) = (a) Find the steady state solution, us(1), for the PDE. (b) Let Uſz,t) = u(?, t) – us(T). Derive a PDE plus boundary and initial conditions for U(2,t). Show your working. (c) Use separation of variables to solve the resulting problem for U. You may leave the inner products...
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...
Problem #2115 Points) Solve the following initial-boundary-value prob- lem: u(0,t) = 1 uz(1,1) + ßu(1,1) = 1 BCs: 0 < t < oo 0 IC: u(z,0)= sin(nx)+x, 1 x by transforming it into homogeneous...
Problem #2115 Points) Solve the following initial-boundary-value prob- lem: u(0,t) = 1 uz(1,1) + ßu(1,1) = 1 BCs: 0 < t < oo 0 IC: u(z,0)= sin(nx)+x, 1 x by transforming it into homogeneous BCs and then solving the transformed problem
Problem #2115 Points) Solve the following initial-boundary-value prob- lem: u(0,t) = 1 uz(1,1) + ßu(1,1) = 1 BCs: 0
PDE: Ut = Uxx, -00 < x < 0, t> 0 IC: u(x,0) = 38(x) +...
PDE: Ut = Uxx, -00 < x < 0, t> 0 IC: u(x,0) = 38(x) + 28(x – 6) where is the Dirac delta function (impulse). u(x, t) =
Let u be the solution to the initial boundary value problem for the Heat Equation an(t,r)-301a(t, z), te(0,00), z E (0,3); with initial condition 3 0 and with boundary conditions 6xu(t,0)-0, u(t, 3)...
Let u be the solution to the initial boundary value problem for the Heat Equation an(t,r)-301a(t, z), te(0,00), z E (0,3); with initial condition 3 0 and with boundary conditions 6xu(t,0)-0, u(t, 3) 0 Find the solution u using the expansion with the normalization conditions vn (0)-1, wn(0) 1 a. (3/10) Find the functionsw with index n1 b. (3/10) Find the functions vn with index n1 Un c. (4/10) Find the coefficients cn, with index n 1
Let u be...
1. Solve the following transient heat equation by separation of variable method. aT At x = 0, BC み_Qo Atx=L, T =To IC: At t = 0, T= 1. Solve the following transient heat equation by separat...
1. Solve the following transient heat equation by separation of variable method. aT At x = 0, BC み_Qo Atx=L, T =To IC: At t = 0, T=
1. Solve the following transient heat equation by separation of variable method. aT At x = 0, BC み_Qo Atx=L, T =To IC: At t = 0, T=
1. Wave equation. Consider the wave equation on the finite interval (0, L) PDE BC where Neumann boundary conditions are specified Physically, with Neumann boundary conditions, u(r, t) could represent the height of a fluid that sloshes between two walls. (a) Find the general Fourier series solution by repeating the derivation from class now considering Neumann instead of Dirichlet boundary conditions. Your final solution should be (b) Consider the following general initial conditions u(x, 0)x) IC IC Derive formulas that...
1. Solve the vibrating string problem PDE BC BC IC IC utt T.T Uz(0,t) = 0 u(1,t0 u(x,0cos(3T) 14(2.0) = x
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...
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...
=T 20 marks) Consider the following PDE with boundary and initial conditions: U = Upx + ur, for 0<x< 1 and to with u(0,t) = 1, u(1,t) = 0, u(1,0) = (a) Find the steady state solution, us(1), for the PDE. (b) Let Uſz,t) = u(?, t) – us(T). Derive a PDE plus boundary and initial conditions for U(2,t). Show your working. (c) Use separation of variables to solve the resulting problem for U. You may leave the inner products...
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...
Problem #2115 Points) Solve the following initial-boundary-value prob- lem: u(0,t) = 1 uz(1,1) + ßu(1,1) = 1 BCs: 0 < t < oo 0 IC: u(z,0)= sin(nx)+x, 1 x by transforming it into homogeneous BCs and then solving the transformed problem
Problem #2115 Points) Solve the following initial-boundary-value prob- lem: u(0,t) = 1 uz(1,1) + ßu(1,1) = 1 BCs: 0
PDE: Ut = Uxx, -00 < x < 0, t> 0 IC: u(x,0) = 38(x) + 28(x – 6) where is the Dirac delta function (impulse). u(x, t) =
Let u be the solution to the initial boundary value problem for the Heat Equation an(t,r)-301a(t, z), te(0,00), z E (0,3); with initial condition 3 0 and with boundary conditions 6xu(t,0)-0, u(t, 3) 0 Find the solution u using the expansion with the normalization conditions vn (0)-1, wn(0) 1 a. (3/10) Find the functionsw with index n1 b. (3/10) Find the functions vn with index n1 Un c. (4/10) Find the coefficients cn, with index n 1
Let u be...
1. Solve the following transient heat equation by separation of variable method. aT At x = 0, BC み_Qo Atx=L, T =To IC: At t = 0, T=
1. Solve the following transient heat equation by separation of variable method. aT At x = 0, BC み_Qo Atx=L, T =To IC: At t = 0, T=
Most questions answered within 3 hours.
-
What is the purpose of the 2' hydroxyl group in RNA? What is
the reason this...
asked 7 minutes ago -
You currently have 20,000X ethidium bromide. You want to make
250 mL of 1X ethidium bromide...
asked 20 minutes ago -
What mass of lead is needed to absorb 348 J of heat if the temp
of...
asked 22 minutes ago -
Explain the difference between an auction with reserve
and an auction without reserve. if not specified,...
asked 24 minutes ago -
Write the net ionic equation for the precipitation reaction that
occurs when aqueous solutions of aluminum...
asked 28 minutes ago -
How do we find the slope distance, given the horizontal distance
and the zenith angle?
For...
asked 26 minutes ago -
The table to the right lists probabilities for the corresponding
numbers of girls in three births....
asked 38 minutes ago -
The inverse demand function for good X is P = 5−0.05Q. The
firm’s cost curve is...
asked 36 minutes ago -
The Fresh Connection is really pushing the new line of juice
products. Given that it takes...
asked 42 minutes ago -
An acute decrease in mean arterial pressure (by getting up very
quickly, for instance) will cause...
asked 40 minutes ago -
Is the pH of solutions important when using the Fluoride ISE? If
so, why?
asked 44 minutes ago -
Producer surplus is:
a.
always equal to consumer surplus.
b.
the amount paid to sellers above...
asked 45 minutes ago