State mathematical formulation of the problem (balance equation and boundary conditions) (3 points) Determine the type of boundary conditions (essential or natural) (2 points)
Homework Answers
Add Answer to:
q-q(x) L=1 State mathematical formulation of the problem (balance equation and boundary conditions) (3 points) Determin...
Solve the heat equation ut = for all time (zero Neumann boundary conditions), if the initial...
Solve the heat equation ut = for all time (zero Neumann boundary conditions), if the initial temperature is given by (ax)xsin TX. First, formulate the mathematical problem and complete the three steps as described 10uforarod of length 1 with both ends insulated Mathematical Formulation Step 1 Derive an expression for all nontrivial product (separated) solutions including an eigenvalue problem satisfying the boundary conditions Step 2: Solve the eigenvalue problem Step 3: Use the superposition principle and Fourier series to find...
Consider the 1D wave equation Ye = a?yrz (1) with boundary conditions y(x 0,t) 0; y(x...
Consider the 1D wave equation Ye = a?yrz (1) with boundary conditions y(x 0,t) 0; y(x = L, t) = 0; y(r, t = 0) - f(x); y(r,t 0) 0. (2) Use separation of variables to convert the PDE into 2 ODEs. Clearly state the boundary conditions for the 2 ODEs
Consider the 1D wave equation Ye = a?yrz (1) with boundary conditions y(x 0,t) 0; y(x = L, t) = 0; y(r, t = 0) - f(x); y(r,t 0)...
2. Construct the weak form of the following linear equation. Are the boundary conditions “essenti...
2. Construct the weak form of the following linear equation. Are
the boundary conditions “essential” or “natural”?
Il (x +r) --sin (x ) OSxst dx du ax 11 (0)=0 =0
Il (x +r) --sin (x ) OSxst dx du ax 11 (0)=0 =0
Solve the heat equation ut = 10uct for a rod of length 1 with both ends...
Solve the heat equation ut = 10uct for a rod of length 1 with both ends insulated for all time (zero Neumann boundary conditions), if the initial temperature is given by (2) = x+sin ax. First, formulate the mathematical problem and complete the three steps as described. Mathematical Formulation Step 1: Derive an expression for all nontrivial product (separated) solutions including an eigenvalue problem satisfying the boundary conditions Step 2: Solve the eigenvalue problem Step 3: Use the superposition principle...
3. Find all critical points of dt dt with the constraint PP = 8 0 (c and boundary conditions x(0) - 0, x(1)- 3. Hint: Write the Euler Lagrange equation (there is no dependence on t), and then use the...
3. Find all critical points of dt dt with the constraint PP = 8 0 (c and boundary conditions x(0) - 0, x(1)- 3. Hint: Write the Euler Lagrange equation (there is no dependence on t), and then use the boundary conditions and the constraint to reach a system of 2 equations (with quadratic terms) of two unknown constants a, b Solve it by first finding a quadratic equation for a/b
3. Find all critical points of dt dt with...
solve problem #1 depending on the given information Consider the following 1D second order elliptic equation with Dirichlet boundary conditions du(x) (c(x)du ) = f(x) (a $15 b), u(a) = ga, u(b) = gb...
solve problem #1 depending on the given information
Consider the following 1D second order elliptic equation with Dirichlet boundary conditions du(x) (c(x)du ) = f(x) (a $15 b), u(a) = ga, u(b) = gb dr: where u(x) is the unknown function, ga and gb are the Dirichlet boundary values, c(x) is a given coefficient function and f(x) is a given source function. See the theorem 10.1 in the textbook for the existence and uniqueness of the solution. 1.1 Weak Formulation...
3. Consider the damped wave equation with boundary conditions where 0 < β < 21tc/ L....
3. Consider the damped wave equation with boundary conditions where 0 < β < 21tc/ L. (i) Explain the physical meaning of the term-8ut. Why is β > 0? (ii) Explain the physical meaning of the boundary conditions. ii) Using separation of variables and superposition, solve the initial value problem (iv) What is the long-time behavior of the solution?
Section 1.3 3. a. Solve the following initial boundary value problem for the heat equation 0x<L...
Section 1.3 3. a. Solve the following initial boundary value problem for the heat equation 0x<L t0 at u(r, 0) f() u(0, t)u(L, t) 0, t>0, 9Tr when f(r)6 sin L b. Solve the following initial boundary value problem for the diffusion equation au D 0 L t0 at u(r, 0) f() (0, t) (L, t) 0, t 0, x < L/2 0. when f(r) r > L/2. 1
Section 1.3 3. a. Solve the following initial boundary value problem...
Problem 2. Solve the following ID wave equation: Ott(x,t) = 0xx(x, t) with the boundary conditions...
Problem 2. Solve the following ID wave equation: Ott(x,t) = 0xx(x, t) with the boundary conditions 0(0,t) = 0x(1,t) = 0, where 0(x, t) refers to the twist angle of a uniform rod of unit length. Problem 3. Show that the solution of the partial differential equation (Laplace equation),
Computer assignment Computer assignment Consider two dimensional, steady state conduction in a square cross section. Discretization...
Computer assignment
Computer assignment Consider two dimensional, steady state conduction in a square cross section. Discretization is as shown Δx=Δy Requires 1- determine temperature at node 1 through 16. 2-determine heat transfer rates. 3-determine location and value of T"max" 4-check energy balance. The details for boundary conditions in the picture Need code written in EES ( engineering equation solver) Will be helpful if there is: Mathematical formulation and Numerical solution procedure. Thanks
Solve the heat equation ut = for all time (zero Neumann boundary conditions), if the initial temperature is given by (ax)xsin TX. First, formulate the mathematical problem and complete the three steps as described 10uforarod of length 1 with both ends insulated Mathematical Formulation Step 1 Derive an expression for all nontrivial product (separated) solutions including an eigenvalue problem satisfying the boundary conditions Step 2: Solve the eigenvalue problem Step 3: Use the superposition principle and Fourier series to find...
Consider the 1D wave equation Ye = a?yrz (1) with boundary conditions y(x 0,t) 0; y(x = L, t) = 0; y(r, t = 0) - f(x); y(r,t 0) 0. (2) Use separation of variables to convert the PDE into 2 ODEs. Clearly state the boundary conditions for the 2 ODEs
Consider the 1D wave equation Ye = a?yrz (1) with boundary conditions y(x 0,t) 0; y(x = L, t) = 0; y(r, t = 0) - f(x); y(r,t 0)...
2. Construct the weak form of the following linear equation. Are
the boundary conditions “essential” or “natural”?
Il (x +r) --sin (x ) OSxst dx du ax 11 (0)=0 =0
Il (x +r) --sin (x ) OSxst dx du ax 11 (0)=0 =0
Solve the heat equation ut = 10uct for a rod of length 1 with both ends insulated for all time (zero Neumann boundary conditions), if the initial temperature is given by (2) = x+sin ax. First, formulate the mathematical problem and complete the three steps as described. Mathematical Formulation Step 1: Derive an expression for all nontrivial product (separated) solutions including an eigenvalue problem satisfying the boundary conditions Step 2: Solve the eigenvalue problem Step 3: Use the superposition principle...
3. Find all critical points of dt dt with the constraint PP = 8 0 (c and boundary conditions x(0) - 0, x(1)- 3. Hint: Write the Euler Lagrange equation (there is no dependence on t), and then use the boundary conditions and the constraint to reach a system of 2 equations (with quadratic terms) of two unknown constants a, b Solve it by first finding a quadratic equation for a/b
3. Find all critical points of dt dt with...
solve problem #1 depending on the given information
Consider the following 1D second order elliptic equation with Dirichlet boundary conditions du(x) (c(x)du ) = f(x) (a $15 b), u(a) = ga, u(b) = gb dr: where u(x) is the unknown function, ga and gb are the Dirichlet boundary values, c(x) is a given coefficient function and f(x) is a given source function. See the theorem 10.1 in the textbook for the existence and uniqueness of the solution. 1.1 Weak Formulation...
3. Consider the damped wave equation with boundary conditions where 0 < β < 21tc/ L. (i) Explain the physical meaning of the term-8ut. Why is β > 0? (ii) Explain the physical meaning of the boundary conditions. ii) Using separation of variables and superposition, solve the initial value problem (iv) What is the long-time behavior of the solution?
Section 1.3 3. a. Solve the following initial boundary value problem for the heat equation 0x<L t0 at u(r, 0) f() u(0, t)u(L, t) 0, t>0, 9Tr when f(r)6 sin L b. Solve the following initial boundary value problem for the diffusion equation au D 0 L t0 at u(r, 0) f() (0, t) (L, t) 0, t 0, x < L/2 0. when f(r) r > L/2. 1
Section 1.3 3. a. Solve the following initial boundary value problem...
Problem 2. Solve the following ID wave equation: Ott(x,t) = 0xx(x, t) with the boundary conditions 0(0,t) = 0x(1,t) = 0, where 0(x, t) refers to the twist angle of a uniform rod of unit length. Problem 3. Show that the solution of the partial differential equation (Laplace equation),
Computer assignment
Computer assignment Consider two dimensional, steady state conduction in a square cross section. Discretization is as shown Δx=Δy Requires 1- determine temperature at node 1 through 16. 2-determine heat transfer rates. 3-determine location and value of T"max" 4-check energy balance. The details for boundary conditions in the picture Need code written in EES ( engineering equation solver) Will be helpful if there is: Mathematical formulation and Numerical solution procedure. Thanks
Most questions answered within 3 hours.
-
Use the following set of observed frequencies to test the
independence of the two variables. Variable...
asked 14 minutes ago -
Two kg of ice at -15 °C are placed in a 2 kg bath of water...
asked 14 minutes ago -
Describe the following with suitable
examples.
1- Security Policy Heterogeneity
2-Security Model Heterogeneity
3-Security Mechanism Heterogeneity...
asked 15 minutes ago -
Please Identify the Term "Determinism" in Psychology
asked 14 minutes ago -
The table below represents the number of republicans, democrats
and independent voting on a specific issue....
asked 19 minutes ago -
List and compare different forms of passive transport and active
transport.
asked 27 minutes ago -
In Netherland Dwarf rabbits, dwarf size is determined by allele
N, and normal-size by allele n....
asked 33 minutes ago -
During Heaton Company’s first two years of operations, it
reported absorption costing net operating income as...
asked 48 minutes ago -
Consider testing the
hypotheses:
H0: p = 0.56
H1: p > 0.56
where p is
the...
asked 51 minutes ago -
In a two-factor analysis of variance a main effect is defined as
____.
a. the unique...
asked 58 minutes ago -
A bank's loan officer rates applicants for credit. The ratings
are normally distributed with a mean...
asked 59 minutes ago -
Fill in the following information for Adipic Acid: molecular
weight, g or ml, mole, melting point,...
asked 1 hour ago