Applied Numerical Methods with MATLAB for Engineers and Scientists 4th. Edition by Steven C. Chapra Dr. | 9780073397962 | 0073397962 | Holooly

Numerical Methods

Applied Numerical Methods with MATLAB for Engineers and Scientists

144 SOLVED PROBLEMS

Question: 24.8

Use bvp4c to solve the following second-order ODE d²y/dx² + y = 1 subject to the boundary conditions y(0) = 1 y(π ∕ 2) = 0 ...

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Question: 24.7

Use the finite-difference approach to simulate the temperature of a heated rod subject to both convection and radiation: 0 = d²T/dx² + h′(T∞ − T )+σ′^′( T∞^4−T^4) where σ′ = 2.7 × 10^−9 K^−3 m^−2, L = 10 m, h′ = 0.05 m^−2, T∞ = 200 K, T(0) = 300 K, and T(10) = 400 K. Use four interior ...

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Using Eq. (24.19) we can successively solve for th...

Question: 24.6

Generate the finite-difference solution for a 10-m rod with Δ x = 2 m, h′ = 0.05 m^−2, T∞ = 200 K, and the boundary conditions: Ta′ = 0 and Tb = 400 K. Note that the first condition means that the slope of the solution should approach zero at the rod’s left end. Aside from this case, also generate ...

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Equation (24.18) can be used to represent node 0 a...

Question: 24.5

Use the finite-difference approach to solve the same problem as in Examples 24.1 and 24.2. Use four interior nodes with a segment length of Δ x = 2 m. ...

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Question: 24.4

Although it served our purposes for illustrating the shooting method,Eq. (24.6) was not a completely realistic model for a heated rod. For one thing, such a rod would lose heat by mechanisms such as radiation that are nonlinear. Suppose that the following nonlinear ODE is used to simulate the ...

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Question: 24.3

Use the shooting method to solve Eq. (24.6) for the rod in Example 24.1:L = 10 m, h′ = 0.05 m−2 [ h = 1 J/(m2 · K · s), r = 0.2 m, k = 200 J/(s · m · K)], T∞ = 200 K, and T(10) = 400 K. However, for this case, rather than having a fixed temperature of 300 K, the left end is subject to convection as ...

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Question: 24.2

Use the shooting method to solve Eq. (24.6) for the same conditions as Example 24.1: L = 10 m, h′ = 0.05 m^−2, T∞ = 200 K, T (0) = 300 K, and T (10) = 400 K. ...

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Question: 23.CS.5

The Roman natural philosopher, Pliny the Elder, purportedly had an intermittent fountain in his garden. As in Fig. 23.12, water enters a cylindrical tank at a constant flow rate Qin and fills until the water reaches yhigh. At this point, water siphons out of the tank through a circular discharge ...

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Question: 24.1

Use calculus to solve Eq. (24.6) for a 10-m rod with h′ = 0.05 m^−2[h = 1 J/(m² · K · s), r = 0.2 m, k = 200 J/(s · m · K)], T∞ = 200 K, and the boundary conditions: T (0) =300 K T (10) = 400 K ...

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This ODE can be solved in a number of ways. A stra...

Question: 23.7

Determine the position and velocity of a bungee jumper with the following parameters: L = 30 m, g = 9.81 m/s², m = 68.1 kg, cd = 0.25 kg/m, k = 40 N/m, and γ = 8 N · s/m. Perform the computation from t = 0 to 50 s and assume that the initial conditions are x(0) = υ(0) = 0. ...

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