use the following two points boundary value problem;
see attached picture of the question.
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Use the following two points boundary value problem; see attached picture of the question.
2. Two-point boundary value problem with Dirichlet condition. Consider the two-point boundary val...
2. Two-point boundary value problem with Dirichlet condition. Consider the two-point boundary value problem у" = х-уз, у(0) = 0, y(1) = 0. Approximate y'" by (yn-1-2yn ynt1)/Az2 and write the corresponding discretization for this BVP. Take N 4; write the nonlinear system of equations F(y) 0 for the unknowns yi, уг, уз, y4-What is the Jacobian for the problem? Once you have the Jacobian, how do you perform one Newton iteration to solve F(y)-0?
2. Two-point boundary value problem...
Question 3: BVP with periodic boundary conditions. Part I: Solve the following boundary value problem (BVP)...
Question 3: BVP with periodic boundary conditions. Part I: Solve the following boundary value problem (BVP) where y(x,t) is defined for 0<x<. You must show all of your work (be sure to explore all possible eigenvalues). агу д?у 4 axat2 Subject to conditions: = y(x,0) = 4 sin 6x ayi at = 0 y(0) = 0 y(T) = 0 Solution: y(x, t) = Do your work on the next page. Part II: Follow up questions. You may answer these questions...
3. (20 points) Denote u(ar, y) the steady-state temperature in a rectangle area 0 z 10,...
3. (20 points) Denote u(ar, y) the steady-state temperature in a rectangle area 0 z 10, 0yS 1. Find the temperature in the rectangle if the temperature on the up side is kept at 0°, the lower side at 10° while the temperature on the left side is S0)= sin(y) and the right side is insulated. Answer the following questions. (a) (10 points) Write the Dirichlet problem including the Laplace's equation in two dimensions and the boundary conditions. (b) (10...
Solve the boundary value problem
Solve the boundary value problem $$ \begin{gathered} y^{\prime \prime \prime}=-\frac{1}{x} y^{\prime \prime}+\frac{1}{x^{2}} y^{\prime}+0.1\left(y^{\prime}\right)^{3} \\ y(1)=0 \quad y^{\prime \prime}(1)=0 \quad y(2)=1 \end{gathered} $$Use difference equations method. You can get help from matlab for solving the system.
Discretization, ODE solving, condition number. Consider the differential equation 5y"(x) - 2y'(x) +10y(x)0 on the interval x E [0,10] with boundary conditions y(0)2 and y (10) 3 we set up a f...
Discretization, ODE solving, condition number. Consider the differential equation 5y"(x) - 2y'(x) +10y(x)0 on the interval x E [0,10] with boundary conditions y(0)2 and y (10) 3 we set up a finite difference scheme as follows. Divide [0,10] into N-10 sub-intervals, i.e. {xo, X1, [0,1,. 10. Denote xi Xo + ih (here, h- 1) and yi E y(x). Approximate the derivatives as follows X10- 2h we have the following equations representing the ODE at each point Xi ,i = 1,...
Q2 Given the following heat conduction initial-boundary value problem of a thin homogeneous rod, where ?(?,?)...
Q2 Given the following heat conduction
initial-boundary value problem of a thin homogeneous rod, where
?(?,?) represents the temperature. 9??? = ?? ; 0 < ? < 6; ?
> 0; B. C. : ?? (0,?) = 0; ?? (6,?) = 0; ? > 0; I. C. : ?(?,
0) = 12 + 5??? ( ? 6 ?) − 4???(2??); 0 < ? < 6 (a) When ? =
0, what would be the temperature at ? = 3? (Use...
Q2 Given the following heat conduction initial-boundary value problem of a thin homogeneous rod, where ?(?,?)...
Q2 Given the following heat conduction initial-boundary value
problem of a thin homogeneous rod, where ?(?,?) represents the
temperature. 9??? = ?? ; 0 < ? < 6; ? > 0; B. C. : ??
(0,?) = 0; ?? (6,?) = 0; ? > 0; I. C. : ?(?, 0) = 12 + 5??? ( ?
6 ?) − 4???(2??); 0 < ? < 6 (a) When ? = 0, what would be the
temperature at ? = 3? (Use...
Consider these two boundary-value problems: Show that if x is a solution of boundary-value problem,... clear steps and brief explanation please 7. Consider these two boundary-value problems: . x-f (t...
Consider these two boundary-value problems: Show that if x is a
solution of boundary-value problem,...
clear steps and brief explanation please
7. Consider these two boundary-value problems: . x-f (t, x, x') x(a)ax(b) B Show that if x is a solution of boundary-value problem ii, then the function y(t) - x((t- a)/h) solves boundary-value problem i, where h b- a.
7. Consider these two boundary-value problems: . x-f (t, x, x') x(a)ax(b) B Show that if x is a solution...
Question 12) Solve the boundary value problem using a program/script that applied the shooting me...
Please provide the program in Matlab.
Question 12) Solve the boundary value problem using a program/script that applied the shooting method. (t) + y()-8 with the boundary conditions of y(0)-0 and y(10-0. Use ΔΧ-1. Plot on the same axis your solution and the exact solution dt2 t 4 4 dt
Question 12) Solve the boundary value problem using a program/script that applied the shooting method. (t) + y()-8 with the boundary conditions of y(0)-0 and y(10-0. Use ΔΧ-1. Plot on...
Q2 Given the following heat conduction initial-boundary value problem of a thin homogeneous rod, where ?(?,?)...
Q2 Given the following heat conduction initial-boundary value problem of a thin homogeneous rod, where ?(?,?) represents the temperature. 9??? = ?? ; 0 < ? < 6; ? > 0; B. C. : ?? (0,?) = 0; ?? (6,?) = 0; ? > 0; I. C. : ?(?, 0) = 12 + 5??? ( ? 6 ?) − 4???(2??); 0 < ? < 6 (a) When ? = 0, what would be the temperature at ? = 3? (Use...
2. Two-point boundary value problem with Dirichlet condition. Consider the two-point boundary value problem у" = х-уз, у(0) = 0, y(1) = 0. Approximate y'" by (yn-1-2yn ynt1)/Az2 and write the corresponding discretization for this BVP. Take N 4; write the nonlinear system of equations F(y) 0 for the unknowns yi, уг, уз, y4-What is the Jacobian for the problem? Once you have the Jacobian, how do you perform one Newton iteration to solve F(y)-0?
2. Two-point boundary value problem...
Question 3: BVP with periodic boundary conditions. Part I: Solve the following boundary value problem (BVP) where y(x,t) is defined for 0<x<. You must show all of your work (be sure to explore all possible eigenvalues). агу д?у 4 axat2 Subject to conditions: = y(x,0) = 4 sin 6x ayi at = 0 y(0) = 0 y(T) = 0 Solution: y(x, t) = Do your work on the next page. Part II: Follow up questions. You may answer these questions...
3. (20 points) Denote u(ar, y) the steady-state temperature in a rectangle area 0 z 10, 0yS 1. Find the temperature in the rectangle if the temperature on the up side is kept at 0°, the lower side at 10° while the temperature on the left side is S0)= sin(y) and the right side is insulated. Answer the following questions. (a) (10 points) Write the Dirichlet problem including the Laplace's equation in two dimensions and the boundary conditions. (b) (10...
Solve the boundary value problem $$ \begin{gathered} y^{\prime \prime \prime}=-\frac{1}{x} y^{\prime \prime}+\frac{1}{x^{2}} y^{\prime}+0.1\left(y^{\prime}\right)^{3} \\ y(1)=0 \quad y^{\prime \prime}(1)=0 \quad y(2)=1 \end{gathered} $$Use difference equations method. You can get help from matlab for solving the system.
Discretization, ODE solving, condition number. Consider the differential equation 5y"(x) - 2y'(x) +10y(x)0 on the interval x E [0,10] with boundary conditions y(0)2 and y (10) 3 we set up a finite difference scheme as follows. Divide [0,10] into N-10 sub-intervals, i.e. {xo, X1, [0,1,. 10. Denote xi Xo + ih (here, h- 1) and yi E y(x). Approximate the derivatives as follows X10- 2h we have the following equations representing the ODE at each point Xi ,i = 1,...
Q2 Given the following heat conduction
initial-boundary value problem of a thin homogeneous rod, where
?(?,?) represents the temperature. 9??? = ?? ; 0 < ? < 6; ?
> 0; B. C. : ?? (0,?) = 0; ?? (6,?) = 0; ? > 0; I. C. : ?(?,
0) = 12 + 5??? ( ? 6 ?) − 4???(2??); 0 < ? < 6 (a) When ? =
0, what would be the temperature at ? = 3? (Use...
Q2 Given the following heat conduction initial-boundary value
problem of a thin homogeneous rod, where ?(?,?) represents the
temperature. 9??? = ?? ; 0 < ? < 6; ? > 0; B. C. : ??
(0,?) = 0; ?? (6,?) = 0; ? > 0; I. C. : ?(?, 0) = 12 + 5??? ( ?
6 ?) − 4???(2??); 0 < ? < 6 (a) When ? = 0, what would be the
temperature at ? = 3? (Use...
Consider these two boundary-value problems: Show that if x is a
solution of boundary-value problem,...
clear steps and brief explanation please
7. Consider these two boundary-value problems: . x-f (t, x, x') x(a)ax(b) B Show that if x is a solution of boundary-value problem ii, then the function y(t) - x((t- a)/h) solves boundary-value problem i, where h b- a.
7. Consider these two boundary-value problems: . x-f (t, x, x') x(a)ax(b) B Show that if x is a solution...
Please provide the program in Matlab.
Question 12) Solve the boundary value problem using a program/script that applied the shooting method. (t) + y()-8 with the boundary conditions of y(0)-0 and y(10-0. Use ΔΧ-1. Plot on the same axis your solution and the exact solution dt2 t 4 4 dt
Question 12) Solve the boundary value problem using a program/script that applied the shooting method. (t) + y()-8 with the boundary conditions of y(0)-0 and y(10-0. Use ΔΧ-1. Plot on...
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