Numerical Analysis 10th Edition solutions

Numerical Analysis 10
Use the Extrapolation Algorithm with tolerance TOL I0-4 , hmax 0.25, and hmin 0.05 to approximate the solutions to the following initial-value problems. Compare the results to the actual values. a. y' - re3 ' - 2y, 0 < r < I, >-(0) -- 0; actual solution y{t) ^le3 " - ^e3 ' + ^e-2'. b. /= l + (r

Numerical Analysis 10
Use the Extrapolation Algorithm with TOL 10~4 to approximate the solutions to the following initial-value problems: a. y' (y/t)2 + y/t, I < t < 1-2, y(l) = 1, with hmax 0.05 and hmin 0.02. b. y' = sin r + e - ', 0 < r < 1, y(0) = 0, with hmax = 0.25 and hmin = 0.02. c. y' = (y2 + y)/t, 1 < r < 3,

Numerical Analysis 10
Use the Extrapolation Algorithm with tolerance TOL 10-6 , hmax 0.5, and hmin 0.05 to approximate the solutions to the following initial-value problems. Compare the results to the actual values. a. y' y/t - (y/t)2 , 1 < ? < 4, ^(l) = 1; actual solution y(t) = t/(\ +ln/). b. = 1 + y/t + {y/t)1 , 1

Numerical Analysis 10
Use the Extrapolation Algorithm with tolerance TOL = 10~6 , hmax = 0.5, and hmin = 0.05 to approximate the solutions to the following initial-value problems. Compare the results to the actual values. , 2 2ly (2/ + 1) a. y = t2 + \ ' 0 ^ ? 5 3- >'(0) = 1; actual solution y = ^ ^ . y 2 . 1 1 ^ ^ A ./1

Numerical Analysis 10
Suppose a wolf is chasing a rabbit. The path ofthe wolftoward the rabbit is called a curve of pursuit. Assume the wolf runs at the constant speed a and the rabbit at the constant speed /I. Let the wolf begin at time / = 0 at the origin and the rabbit at the point (0, 1). Assume the rabbit runs up the

Numerical Analysis 10
The Gompertz population model was described in Exercise 26 ofSection 2.3. The population is given by P{t) = PLe-ce ~ k ' where Pi, c, and A: > 0 are constants and P{t) isthe population attime t. P(t) satisfies the differential equation P'(t) = k fin PL - In P{t)] P{t). a. Using / = 0 as 1960 and the