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Show that the Sturm-Liouville differential operatorp(x)+q(x) subject to +q(x) subiect to Dirichlet, Neumann or mixed boundary...
1. Consider the non-Sturm-Liouville differential equation Multiply this equation by H(x). Determi...
#2 ONLY PLEASE
1. Consider the non-Sturm-Liouville differential equation Multiply this equation by H(x). Determine H(x) such that the equation may be reduced to the standard Sturm-Liouville form: do Given a(z), 3(2), and 7(2), what are p(x), σ(x), and q(x) 2. Consider the eigenvalue problem (a) Use the result from the previous problem to put this in Sturm-Liouville form (b) Using the Rayleigh quotient, show that λ > 0. (c) Solve this equation subject to the boundary conditions and determine...
2. (Sturm-Liouville Theory) Consider the following linear homogeneous second-order differential e...
2. (Sturm-Liouville Theory) Consider the following linear homogeneous second-order differential equation and boundary conditions v(T where a and b are finite, p(x), p(x,)) are real and continuous on [a, b), and p(x),w(x) > 0 on a,b]. Show that two distinct solutions to this ODE, Pm(z) and (x), are orthogonal to each other on the interval [a,b]. That is, prove the following relationship 0
2. (Sturm-Liouville Theory) Consider the following linear homogeneous second-order differential equation and boundary conditions v(T where a...
3. (10 Points, part III) Consider the Sturm-Liouville differential equation where the coefficients p(z), q(z), and...
3. (10 Points, part III) Consider the Sturm-Liouville differential equation where the coefficients p(z), q(z), and σ(z) are real and continous on la, b , and p(2) and σ(z) are strictly positive for all a,b (a) Derive the Rayleigh quotient λ from (2). b) What does this quotient describe? Give two examples of applications for this formula. (c) what are the neces,ary conditions for λ > 0 to be satisfied? (d) Recall that the minimum value of the Rayleigh quotient...
Please show steps. Use an energy argument to show that the eigenvalues of the Sturm-Liouville Problem...
Please show steps.
Use an energy argument to show that the eigenvalues of the Sturm-Liouville Problem on (0, L) given by X"(x)--AX(x), X,(0) = 0, X'(L) = 0. 0 < x < L, are non-negative, i.e., course Moodle page. > 0. Note that an example of the energy method is available on the 1
Consider the variable ject to Dirichlet boundary conditions at x = 0 and x = 1, Show that if we s...
Consider the variable ject to Dirichlet boundary conditions at x = 0 and x = 1, Show that if we solve this problem using the MOL to get Av then A is symmetric and negative definite. Hint Gerschgorin's theorem may be useful for this last part
Consider the variable ject to Dirichlet boundary conditions at x = 0 and x = 1, Show that if we solve this problem using the MOL to get Av then A is symmetric and...
the interval 0 < x < T 3.1.2. Find all separable eigensolutions to the heat equation...
the interval 0 < x < T 3.1.2. Find all separable eigensolutions to the heat equation ut subject to (b) mixed boundary conditions u(t, 0) 0, u(t, ) = 0; (c) Neumann boundary conditions u(t,0) = 0, u (t, 7) = 0. = rTr On (a) homogeneous Dirichlet boundary conditions u(t, 0) = 0, u(t, ) = 0;
the interval 0
Plz solve Part (B) & Part (C) with all the detailed clear steps and bcz I...
Plz solve Part (B) & Part (C) with all the detailed clear
steps and bcz I don't understand them at all
i
need it in 4-8 hrs plz
with confident sol
EXERCISES 5.5 5.5.1. A Sturm-Liouville eigenvalue problem is called self-adjoint if b dv dx du dac = 0 р u a because then SuL(v) - VL(u)] da = 0 for any two functions u and v satisfying the boundary conditions. Show that the following yield self-adjoint problems: (a) 7(0)...
Given the following heat conduction initial-boundary value problem of a thin homogeneous rod, where u(x, t)...
Given the following heat conduction initial-boundary value problem of a thin homogeneous rod, where u(x, t) represents the temperature. 9uxx = Uti 0<x< 6; t> 0; B.C.: ux(0,t) = 0; ux(6,t) = 0; t> 0; 1. C.: u(x, 0) = 12 + scos (6x) – 4cos(21x); 0<x< 6 (a) When t = 0, what would be the temperature at x = 3? (Use the initial condition.) (3 marks) (b) Determine whether the boundary conditions in this case is Dirichlet, Neumann,...
Q2 Given the following heat conduction initial-boundary value problem of a thin homogeneous rod, where u(x,...
Q2 Given the following heat conduction initial-boundary value problem of a thin homogeneous rod, where u(x, t) represents the temperature. 9uxx = ut; 0 < x < 6; t> 0; B.C.: ux(0,t) = 0; uz(6,t) = 0; t>0; I. C.: u(x,0) = 12 + 5cos (6x) – 4cos(21x); 0<x< 6 (a) When t = 0, what would be the temperature at x = 3? (Use the initial condition.) (b) Determine whether the boundary conditions in this case is Dirichlet, Neumann,...
(1 point) Use eigenvalues and elgenfunction expansion expansion to solve the mixed Dirichlet- Neumann problem for...
(1 point) Use eigenvalues and elgenfunction expansion expansion to solve the mixed Dirichlet- Neumann problem for the Laplace equation Au(x, y) = 0 on the rectangle {(x,y) : 0<x<1, 0<y<1} satisfying the BCS ux(0,y) = 0, ux(1, y) = 0, 0 < y < 1 u(x,0) = x, u(x, 1) = 0, 0<x<1 The solution can be written as The u(x, y) = Covo(y)+(x) + .(x).(y) where on is a normalized eigenfunction for "(x) = 10(x) with x(0) = 0...
#2 ONLY PLEASE
1. Consider the non-Sturm-Liouville differential equation Multiply this equation by H(x). Determine H(x) such that the equation may be reduced to the standard Sturm-Liouville form: do Given a(z), 3(2), and 7(2), what are p(x), σ(x), and q(x) 2. Consider the eigenvalue problem (a) Use the result from the previous problem to put this in Sturm-Liouville form (b) Using the Rayleigh quotient, show that λ > 0. (c) Solve this equation subject to the boundary conditions and determine...
2. (Sturm-Liouville Theory) Consider the following linear homogeneous second-order differential equation and boundary conditions v(T where a and b are finite, p(x), p(x,)) are real and continuous on [a, b), and p(x),w(x) > 0 on a,b]. Show that two distinct solutions to this ODE, Pm(z) and (x), are orthogonal to each other on the interval [a,b]. That is, prove the following relationship 0
2. (Sturm-Liouville Theory) Consider the following linear homogeneous second-order differential equation and boundary conditions v(T where a...
3. (10 Points, part III) Consider the Sturm-Liouville differential equation where the coefficients p(z), q(z), and σ(z) are real and continous on la, b , and p(2) and σ(z) are strictly positive for all a,b (a) Derive the Rayleigh quotient λ from (2). b) What does this quotient describe? Give two examples of applications for this formula. (c) what are the neces,ary conditions for λ > 0 to be satisfied? (d) Recall that the minimum value of the Rayleigh quotient...
Please show steps.
Use an energy argument to show that the eigenvalues of the Sturm-Liouville Problem on (0, L) given by X"(x)--AX(x), X,(0) = 0, X'(L) = 0. 0 < x < L, are non-negative, i.e., course Moodle page. > 0. Note that an example of the energy method is available on the 1
Consider the variable ject to Dirichlet boundary conditions at x = 0 and x = 1, Show that if we solve this problem using the MOL to get Av then A is symmetric and negative definite. Hint Gerschgorin's theorem may be useful for this last part
Consider the variable ject to Dirichlet boundary conditions at x = 0 and x = 1, Show that if we solve this problem using the MOL to get Av then A is symmetric and...
the interval 0 < x < T 3.1.2. Find all separable eigensolutions to the heat equation ut subject to (b) mixed boundary conditions u(t, 0) 0, u(t, ) = 0; (c) Neumann boundary conditions u(t,0) = 0, u (t, 7) = 0. = rTr On (a) homogeneous Dirichlet boundary conditions u(t, 0) = 0, u(t, ) = 0;
the interval 0
Plz solve Part (B) & Part (C) with all the detailed clear
steps and bcz I don't understand them at all
i
need it in 4-8 hrs plz
with confident sol
EXERCISES 5.5 5.5.1. A Sturm-Liouville eigenvalue problem is called self-adjoint if b dv dx du dac = 0 р u a because then SuL(v) - VL(u)] da = 0 for any two functions u and v satisfying the boundary conditions. Show that the following yield self-adjoint problems: (a) 7(0)...
Given the following heat conduction initial-boundary value problem of a thin homogeneous rod, where u(x, t) represents the temperature. 9uxx = Uti 0<x< 6; t> 0; B.C.: ux(0,t) = 0; ux(6,t) = 0; t> 0; 1. C.: u(x, 0) = 12 + scos (6x) – 4cos(21x); 0<x< 6 (a) When t = 0, what would be the temperature at x = 3? (Use the initial condition.) (3 marks) (b) Determine whether the boundary conditions in this case is Dirichlet, Neumann,...
Q2 Given the following heat conduction initial-boundary value problem of a thin homogeneous rod, where u(x, t) represents the temperature. 9uxx = ut; 0 < x < 6; t> 0; B.C.: ux(0,t) = 0; uz(6,t) = 0; t>0; I. C.: u(x,0) = 12 + 5cos (6x) – 4cos(21x); 0<x< 6 (a) When t = 0, what would be the temperature at x = 3? (Use the initial condition.) (b) Determine whether the boundary conditions in this case is Dirichlet, Neumann,...
(1 point) Use eigenvalues and elgenfunction expansion expansion to solve the mixed Dirichlet- Neumann problem for the Laplace equation Au(x, y) = 0 on the rectangle {(x,y) : 0<x<1, 0<y<1} satisfying the BCS ux(0,y) = 0, ux(1, y) = 0, 0 < y < 1 u(x,0) = x, u(x, 1) = 0, 0<x<1 The solution can be written as The u(x, y) = Covo(y)+(x) + .(x).(y) where on is a normalized eigenfunction for "(x) = 10(x) with x(0) = 0...
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