The solution of the given problem using Crank-Nicolson method and also create a table of the exact value, the approximate value and the error at ( x , t ) = ( 0.3 , 1 ) for the given step sizes h = k = 0.1 , 0.05 , 0.025.

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Answer 1

Question

Chapter 8.1, Problem 6CP

a.

To determine

To calculate: The solution of the given problem using Crank-Nicolson method and also create a table of the exact value, the approximate value and the error at (x,t)=(0.3,1) for the given step sizes h=k=0.1,0.05,0.025.

b.

To determine

To find: The solution of the given problem using Crank-Nicolson method and also create a table of the exact value, the approximate value and the error at (x,t)=(0.3,1) for the given step sizes h=k=0.1,0.05,0.025.

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1) and let Xt is stochastic process with WSS and Rxlt t+t) 1) E (X5) = \ 1 2 Show that E (X5 = X 3 = 2 (= = =) Since X is WSSEL 2 3) find E(X5+ X3)² 4) sind E(X5+X2) J=1 ***

Question 1: Let X be a random variable with p.m.f (|x| +1)² x= -2, -1, 0, 1,2 f(x) = C 0, O.W 1. The value of c. 2. The c.d.f. 3. E(X). 4. E(2x+3). 5. E(X²). 6. E(3x²+4). 7. E(X(3X+4)). 8. Var(X). 9. Var (6-3X). 10. Find the m.g.f of the random variable X

Answer 2

Question

Chapter 8.1, Problem 6CP

a.

To determine

To calculate: The solution of the given problem using Crank-Nicolson method and also create a table of the exact value, the approximate value and the error at (x,t)=(0.3,1) for the given step sizes h=k=0.1,0.05,0.025.

b.

To determine

To find: The solution of the given problem using Crank-Nicolson method and also create a table of the exact value, the approximate value and the error at (x,t)=(0.3,1) for the given step sizes h=k=0.1,0.05,0.025.

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Answer 3

Question

Chapter 8.1, Problem 6CP

a.

To determine

To calculate: The solution of the given problem using Crank-Nicolson method and also create a table of the exact value, the approximate value and the error at (x,t)=(0.3,1) for the given step sizes h=k=0.1,0.05,0.025.

b.

To determine

To find: The solution of the given problem using Crank-Nicolson method and also create a table of the exact value, the approximate value and the error at (x,t)=(0.3,1) for the given step sizes h=k=0.1,0.05,0.025.

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Answer 4

Question

Chapter 8.1, Problem 6CP

a.

To determine

To calculate: The solution of the given problem using Crank-Nicolson method and also create a table of the exact value, the approximate value and the error at (x,t)=(0.3,1) for the given step sizes h=k=0.1,0.05,0.025.

b.

To determine

To find: The solution of the given problem using Crank-Nicolson method and also create a table of the exact value, the approximate value and the error at (x,t)=(0.3,1) for the given step sizes h=k=0.1,0.05,0.025.

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Answer 5

Chapter 8.1, Problem 6CP

a.

To determine

To calculate: The solution of the given problem using Crank-Nicolson method and also create a table of the exact value, the approximate value and the error at (x,t)=(0.3,1) for the given step sizes h=k=0.1,0.05,0.025.

b.

To determine

To find: The solution of the given problem using Crank-Nicolson method and also create a table of the exact value, the approximate value and the error at (x,t)=(0.3,1) for the given step sizes h=k=0.1,0.05,0.025.

Answer 6

Chapter 8.1, Problem 6CP

a.

To determine

To calculate: The solution of the given problem using Crank-Nicolson method and also create a table of the exact value, the approximate value and the error at (x,t)=(0.3,1) for the given step sizes h=k=0.1,0.05,0.025.

Answer 7

Chapter 8.1, Problem 6CP

a.

To determine

To calculate: The solution of the given problem using Crank-Nicolson method and also create a table of the exact value, the approximate value and the error at (x,t)=(0.3,1) for the given step sizes h=k=0.1,0.05,0.025.

Answer 8

b.

To determine

To find: The solution of the given problem using Crank-Nicolson method and also create a table of the exact value, the approximate value and the error at (x,t)=(0.3,1) for the given step sizes h=k=0.1,0.05,0.025.

Answer 9

b.

To determine

To find: The solution of the given problem using Crank-Nicolson method and also create a table of the exact value, the approximate value and the error at (x,t)=(0.3,1) for the given step sizes h=k=0.1,0.05,0.025.

Answer 10

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Answer 11

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Answer 12

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Answer 13

Ch. 8.1 - Prove that the functions (a) u(x,t)=e2t+x+e2tx,...Ch. 8.1 - Prove that the functions (a) u(x,t)=etsinx, (b)...Ch. 8.1 - Prove that if f(x) is a degree 3 polynomial, then...Ch. 8.1 - Prob. 4E Ch. 8.1 - Verify the eigenvector equation (8.13).Ch. 8.1 - Show that the nonzero vectors vj in (8.12 ), for...Ch. 8.1 - Prob. 1CP Ch. 8.1 - Consider the equation ut=uxx for 0x1, 0t1 with the...Ch. 8.1 - Prob. 3CP Ch. 8.1 - Use the Backward Difference Method to solve the...

The solution of the given problem using Crank-Nicolson method and also create a table of the exact value, the approximate value and the error at ( x , t ) = ( 0.3 , 1 ) for the given step sizes h = k = 0.1 , 0.05 , 0.025.

Solution Summary: The author explains the Crank-Nicolson method and creates a table of the exact value, the approximate value and the error at (x,t)=(0.3,1) for the given step sizes.

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To calculate: The solution of the given problem using Crank-Nicolson method and also create a table of the exact value, the approximate value and the error at (x,t)=(0.3,1) for the given step sizes h=k=0.1,0.05,0.025.

To find: The solution of the given problem using Crank-Nicolson method and also create a table of the exact value, the approximate value and the error at (x,t)=(0.3,1) for the given step sizes h=k=0.1,0.05,0.025.

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