- 5-10.5.10.1: To prove Theorem 5.20, part (i), show that the hypotheses imply tha...
- 5-10.5.10.2: To prove Theorem 5.20, part (i), show that the hypotheses imply tha...
- 5-10.5.10.3: Use the results of Exercise 31 in Section 5.4 to show that the Rung...
- 5-10.5.10.4: Consider the differential equation y = f (t, y), a t b, y(a) = . a....
- 5-10.5.10.5: Given the multistep method wi+1 = 3 2wi + 3wi1 1 2wi2 + 3h f (ti, w...
- 5-10.5.10.6: Obtain an approximate solution to the differential equation y = y, ...
- 5-10.5.10.7: Investigate stability for the difference method wi+1 = 4wi + 5wi1 +...
- 5-10.5.10.8: Consider the problem y = 0, 0 t 10, y(0) = 0, which has the solutio...
Solutions for Chapter 5-10: Stability
Full solutions for Numerical Analysis (Available Titles CengageNOW) | 8th Edition
Addition property of equality
If u = v and w = z , then u + w = v + z
Additive inverse of a real number
The opposite of b , or -b
Annual percentage yield (APY)
The rate that would give the same return if interest were computed just once a year
See Compound fraction.
Conic section (or conic)
A curve obtained by intersecting a double-napped right circular cone with a plane
Equivalent equations (inequalities)
Equations (inequalities) that have the same solutions.
A subset of a sample space.
See Component form of a vector.
See Mathematical induction.
Multiplication property of inequality
If u < v and c > 0, then uc < vc. If u < and c < 0, then uc > vc
The measure of acidity
See Polar coordinate system.
A variable that is affected by an explanatory variable.
A logarithmic scale used in measuring the intensity of an earthquake.
Angle measure equal to 1/60 of a minute.
Slope-intercept form (of a line)
y = mx + b
Sum of two vectors
<u1, u2> + <v1, v2> = <u1 + v1, u2 + v2> <u1 + v1, u2 + v2, u3 + v3>
The x-value of the right side of the viewing window,.
Usually the third dimension in Cartesian space.
See n factorial.