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Chapter 3: Q 3.7-3E (page 139)
Determine the recursive formulas for the Taylor method of order 4 for the initial value problem.
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A red wine is brought up from the wine cellar, which is a cool 10掳C, and left to breathe in a room of temperature 23掳C. If it takes 10 min for the wine to reach 15掳C, when will the temperature of the wine reach 18掳C?
The solution to the initial value problemcrosses the x-axis at a point in the interval [0,14].By experimenting with the improved Euler鈥檚 method subroutine, determine this point to two decimal places.
The air in a small room 12 ft by 8 ft by 8 ft is 3% carbon monoxide. Starting at t = 0, fresh air containing no carbon monoxide is blown into the room at a rate of . If air in the room flows out through a vent at the same rate, when will the air in the room be 0.01% carbon monoxide?
Fluid Flow. In the study of the no isothermal flow of a Newtonian fluid between parallel plates, the equation\(\frac{{{{\bf{d}}^{\bf{2}}}{\bf{y}}}}{{{\bf{d}}{{\bf{x}}^{\bf{2}}}}}{\bf{ + }}{{\bf{x}}^{\bf{2}}}{{\bf{e}}^{\bf{y}}}{\bf{ = 0,x > 0}}\) , was encountered. By a series of substitutions, this equation can be transformed into the first-order equation\(\frac{{{\bf{dv}}}}{{{\bf{du}}}}{\bf{ = u}}\left( {\frac{{\bf{u}}}{{\bf{2}}}{\bf{ + 1}}} \right){{\bf{v}}^{\bf{3}}}{\bf{ + }}\left( {{\bf{u + }}\frac{{\bf{5}}}{{\bf{2}}}} \right){{\bf{v}}^{\bf{2}}}\). Use the fourth-order Runge鈥揔utta algorithm to approximate \({\bf{v(3)}}\) if \({\bf{v(u)}}\) satisfies\({\bf{v(}}2{\bf{)}} = 0.1\). For a tolerance of, \({\bf{\varepsilon = 0}}{\bf{.0001}}\) use a stopping procedure based on the relative error.
A 400-lb object is released from rest 500 ft above the ground and allowed to fall under the influence of gravity. Assuming that the force in pounds due to air resistance is -10V, where v is the velocity of the object in ft/sec determine the equation of motion of the object. When will the object hit the ground?
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