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Numerical Methods
Numerical Methods for Engineers and Scientists Using MATLAB®
83 SOLVED PROBLEMS
Question: 10.9
FREE VIBRATION OF AN ELASTIC STRING Consider an elastic string of length L = 2 with α = 1 ...
Verified Answer:
We first calculate
\tilde{r}=(k \alpha / h)...
Question: 10.8
CRANK–NICOLSON VERSUS FINITE-DIFFERENCE Consider the temperature distribution problem ...
Verified Answer:
1. We first note that
r=\frac{k \alpha^{2}...
Question: 10.7
CRANK–NICOLSON METHOD; 1D HEAT EQUATION Consider the temperature distribution problem ...
Verified Answer:
With
r=0.4
, Equation 10.32
2...
Question: 10.6
FINITE-DIFFERENCE METHOD; 1D HEAT EQUATION Consider a laterally insulated wire of length ...
Verified Answer:
We first calculate
r=\frac{k \alpha^{2}}{h^...
Question: 10.5
IRREGULAR BOUNDARY Solve uxx + uyy = 0 in the region shown in Figure 10.9 subject to the ...
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Based on the grid shown in Figure 10.9, Equation 1...
Question: 10.4
MIXED PROBLEM Solve the mixed problem described in Figure 10.7 using the grid with h = 1. ...
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Because the Dirichlet boundary conditions are pres...
Question: 10.2
PRADI METHOD For the Dirichlet problem described in Figure 10.4, 1. Perform one complete ...
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1. First half. There are two rows and two columns ...
Question: 10.1
DIRICHLET PROBLEM The Dirichlet problem in Figure 10.2 describes the steady-state ...
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There are three interior mesh points and eight bou...
Question: 9.3
POWER METHODS Find all eigenvalues and eigenvectors of the following matrix using the ...
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Apply the user-defined function PowerMethod to fin...
Question: 8.5
FINITE-DIFFERENCE METHOD, LINEAR BVP WITH MIXED BOUNDARY CONDITIONS Consider the BVP ...
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The interval is 1.5 in length and
\Delta t=...
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