Numerical Methods for Engineers 7th. Edition by Steven C. Chapra, Raymond P. Canale | 9780073397924 | 007339792X | Holooly

Numerical Methods for Engineers [EXP-65371]

197 SOLVED PROBLEMS

Question: 5.6

A Case Where Bisection Is Preferable to False Position Use bisection and false position to locate the root of f(x) = x^10 – 1 between x = 0 and 1.3.

Verified Answer:

Using bisection, the results can be summarized as ...

Question: 25.12

Adaptive Fourth-Order RK Method Use the adaptive fourth-order RK method to integrate y’ = 4e^0.8x – 0.5y from x = 0 to 2 using h = 2 and an initial condition of y(0) = 2. This is the same differential equation that was solved previously in Example 25.5. Recall that the true solutions is y(2)

Verified Answer:

The single prediction with a step of h is computed...

Question: 30.5

ADI Method Use the ADI method to solve for the temperature of the plate in Examples 29.1 and 29.2. At t = 0, assume that the temperature of the plate is zero and the boundary temperatures are instantaneously brought to the levels shown in Fig. 29.4. Employ a time step of 10 s. Recall from

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A value of Δx = 10 cm was employed to characterize...

Question: 2.1

Algorithm for Roots of a Quadratic The roots of a quadratic equation ax^2 + bx + c = 0 can be determined with the quadratic formula, x1 x2 = -b ± √|b^2 – 4ac|/2a (E2.1.1) an algorithm that does the following: Step 1: Prompts the user for the coefﬁcients, a, b, and c. Step 2: Implements the

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We will use a top-down approach to develop our alg...

Question: 12.2

ANALYSIS OF A STATICALLY DETERMINATE TRUSS (CIVIL/ENVIRONMENTAL ENGINEERING) An important problem in structural engineering is that of finding the forces and reactions associated with a statically determinate truss. Figure 12.4 shows an example of such a truss. The forces (F) represent either

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This type of structure can be described as a syste...

Question: 20.4

ANALYSIS OF EXPERIMENTAL DATA (MECHANICAL/AEROSPACE ENGINEERING) Engineering design variables are often dependent on several independent variables. Often this functional dependence is best characterized by multivariate power equations. As discussed in Sec. 17.3, a multiple linear regression of

Verified Answer:

The power equation to be evaluated is

Q=a_{...

Question: 31.1

Analytical Solution for a Heated Rod Solve Eq. (31.12) for a 10-cm rod with boundary conditions of T(0, t) = 40 and T(10, t) = 200 and a uniform heat source of f(x) = 10.

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The equation to be solved is

\frac{d^{2} T}...

Question: 1.1

Analytical Solution to the Falling Parachutist Problem A parachutist of mass 68.1 kg jumps out of a stationary hot air balloon. Use Eq. (1.10) to compute velocity prior to opening the chute. The drag coefficient is equal to 12.5 kg/s.

Verified Answer:

Inserting the parameters into Eq. (1.10) yields [l...

Question: 22.5

Applying Gauss Quadrature to the Falling Parachutist Problem In Example 21.3, we used the multiple-application trapezoidal rule to evaluate d = gm/c ∫0^10[1 – e^-(c/m)t]dt where g = 9.8, c = 12.5, and m = 68.1. The exact value of the integral was determined by calculus to be 289.4351. Recall that

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After modifying the function, the following result...

Question: 7.3

Bairstow’s Method Employ Bairstow’s method to determine the roots of the polynomial f5(x) = x^5 – 3.5x^4 + 2.75x^3 + 2.125x^2 – 3.875x + 1.25 Use initial guesses of r = s = -1 and iterate to a level of εs = 1%.

Verified Answer:

Equations (7.32) and (7.36)

b_n = a_n[/late...

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