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3) Using Crank-Nicolson method, solve urr-11, in u(0, 1)-0 and u(5, 0)-100 for one time step. 0 ...
for the following parabolic PDEs heat equation for one variable d2/dx² u(x,t) = d/dt u(x,t) . Where u(0,t)=0 , u(1,t)=0...
for the following parabolic PDEs heat equation for one variable d2/dx² u(x,t) = d/dt u(x,t) . Where u(0,t)=0 , u(1,t)=0 , u(x,0)=sinπx . Complete using crank nicolson method . With h=0.2 , k=0.02
Solve the following partial differential equations using the Laplace transform method. x〉o, 2 5 ,>0 lim u(x, ,) = 0, u(0,,)-1, 3) İhu Ot x〉o, 2 5 ,>0 lim u(x, ,) = 0, u(0,,)-1, 3) İhu Ot...
Solve the following partial differential equations using the
Laplace transform method.
x〉o, 2 5 ,>0 lim u(x, ,) = 0, u(0,,)-1, 3) İhu Ot
x〉o, 2 5 ,>0 lim u(x, ,) = 0, u(0,,)-1, 3) İhu Ot
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...
Please solve both parts a and b step-by-step using the block reduction method ONLY. Q4 a)...
Please solve both parts a and b step-by-step using the block
reduction method ONLY.
Q4 a) (1 mark) The figure below shows a block diagram of a control system, obtain the transfer function [Y(s)/R(s)]N=0 N(S) R(5) Y(s) Gy(s) Ge(s) H(s) b) (2 marks) The figure below shows a closed-loop system with a reference input and disturbance input. Obtain transfer functions C(s)/R(s) and C(s)/D(S) of the system shown. Use block diagram reduction method only. GF D(S) R(S) Es) U(5) Cs) GC...
5. Solve IBVP 11(0,1)-α, u(L,t)-β u(x,0)- f(x) 120 0Sx SL b) u-100, β-100, f(x)-50x( l-x), L-1,...
5. Solve IBVP 11(0,1)-α, u(L,t)-β u(x,0)- f(x) 120 0Sx SL b) u-100, β-100, f(x)-50x( l-x), L-1, c-1.
5. Find the approximation of y(3) by using Euler's method with a time step h =...
5. Find the approximation of y(3) by using Euler's method with a time step h = 1, where y solves the initial value problem, %3D /(t) = cos(nt)y(t) - t, y(0)= 2. A. -3 B. -4 C. -1 D. 2 E. 4
(3) Solve the following BVP for the Wave Equation using the Fourier Series solution formulac (3a2 u(r, t) 0 u(0, t)0 u(...
(3) Solve the following BVP for the Wave Equation using the Fourier Series solution formulac (3a2 u(r, t) 0 u(0, t)0 u(T, t) 0 u(r, 0) sin(x)2sin(4r) 3sin(8r) (r, 0) 10sin(2x)20sin (3r)- 30sin (5r) (r, t) E (0, ) x (0, 0o) t >0 t > 0 1
(3) Solve the following BVP for the Wave Equation using the Fourier Series solution formulac (3a2 u(r, t) 0 u(0, t)0 u(T, t) 0 u(r, 0) sin(x)2sin(4r) 3sin(8r) (r, 0) 10sin(2x)20sin (3r)-...
3. Solve the wave equation subject to the conditions u(0,t)=0, u(z,t) = 0 at 2 2...
3. Solve the wave equation subject to the conditions u(0,t)=0, u(z,t) = 0 at 2 2 u(x, 0) = 4 =0 at 2 =1
3. Solve the wave equation subject to the conditions u(0,t)=0, u(z,t) = 0 at 2 2 u(x, 0) = 4 =0 at 2 =1
n-1 4. Solve u(1,0) cos(0)+sin(20). 5. Solve n-1 4. Solve u(1,0) cos(0)+sin(20). 5. Solve
n-1 4. Solve u(1,0) cos(0)+sin(20). 5. Solve
n-1 4. Solve u(1,0) cos(0)+sin(20). 5. Solve
Solve the following problem using the Simplex-Method-and show the dictionaries and code in AMPL. subject to 5; x, +2x, +3x, subject to x,+x, +2x, s3; subject to x,.x2,r, 20; Solve the following...
Solve the following problem using the Simplex-Method-and show the dictionaries and code in AMPL. subject to 5; x, +2x, +3x, subject to x,+x, +2x, s3; subject to x,.x2,r, 20;
Solve the following problem using the Simplex-Method-and show the dictionaries and code in AMPL. subject to 5; x, +2x, +3x, subject to x,+x, +2x, s3; subject to x,.x2,r, 20;
Solve the following partial differential equations using the
Laplace transform method.
x〉o, 2 5 ,>0 lim u(x, ,) = 0, u(0,,)-1, 3) İhu Ot
x〉o, 2 5 ,>0 lim u(x, ,) = 0, u(0,,)-1, 3) İhu Ot
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...
Please solve both parts a and b step-by-step using the block
reduction method ONLY.
Q4 a) (1 mark) The figure below shows a block diagram of a control system, obtain the transfer function [Y(s)/R(s)]N=0 N(S) R(5) Y(s) Gy(s) Ge(s) H(s) b) (2 marks) The figure below shows a closed-loop system with a reference input and disturbance input. Obtain transfer functions C(s)/R(s) and C(s)/D(S) of the system shown. Use block diagram reduction method only. GF D(S) R(S) Es) U(5) Cs) GC...
5. Solve IBVP 11(0,1)-α, u(L,t)-β u(x,0)- f(x) 120 0Sx SL b) u-100, β-100, f(x)-50x( l-x), L-1, c-1.
5. Find the approximation of y(3) by using Euler's method with a time step h = 1, where y solves the initial value problem, %3D /(t) = cos(nt)y(t) - t, y(0)= 2. A. -3 B. -4 C. -1 D. 2 E. 4
(3) Solve the following BVP for the Wave Equation using the Fourier Series solution formulac (3a2 u(r, t) 0 u(0, t)0 u(T, t) 0 u(r, 0) sin(x)2sin(4r) 3sin(8r) (r, 0) 10sin(2x)20sin (3r)- 30sin (5r) (r, t) E (0, ) x (0, 0o) t >0 t > 0 1
(3) Solve the following BVP for the Wave Equation using the Fourier Series solution formulac (3a2 u(r, t) 0 u(0, t)0 u(T, t) 0 u(r, 0) sin(x)2sin(4r) 3sin(8r) (r, 0) 10sin(2x)20sin (3r)-...
3. Solve the wave equation subject to the conditions u(0,t)=0, u(z,t) = 0 at 2 2 u(x, 0) = 4 =0 at 2 =1
3. Solve the wave equation subject to the conditions u(0,t)=0, u(z,t) = 0 at 2 2 u(x, 0) = 4 =0 at 2 =1
n-1 4. Solve u(1,0) cos(0)+sin(20). 5. Solve
n-1 4. Solve u(1,0) cos(0)+sin(20). 5. Solve
Solve the following problem using the Simplex-Method-and show the dictionaries and code in AMPL. subject to 5; x, +2x, +3x, subject to x,+x, +2x, s3; subject to x,.x2,r, 20;
Solve the following problem using the Simplex-Method-and show the dictionaries and code in AMPL. subject to 5; x, +2x, +3x, subject to x,+x, +2x, s3; subject to x,.x2,r, 20;
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