# math

posted by .

Consider the initial value problem,

f(x,y) = y(18.06 - y), y(0) = 12.

The exact solution of the problem increases from y(0) =12 to y = 18.06 as x increases without limit.

Determine the minimum upper bound of h for the classical 4th-order Runge Kutta method to be absolutely stable for this problem. Give your answer to 3 decimal places.

Note : You can make use of table (3.1) of Study Unit 2 Numerical Methods for Differential Equations.

## Similar Questions

1. ### math

Hi, I had a question about exponential growth. The problem says: The population in Woonsocket is 43,500. Every year the population increases by 2%. Write the exponential equation that represents this situation. I put that the equation …
2. ### math

in scatterplot comparing x and y, the y-values are along the vertical axis. the line of the best fit is horizontal. which statement best describes relationship between x and y?
3. ### Statistics

As x increases, does the value of r imply that y should tend to increase, decrease, or remain the same?
4. ### Chem

Consider the exothermic reaction CoCl42-(aq) + 6 H2O(l) --> Co(H2O)62+(aq) + 4 Cl -(aq). Will the equilibrium concentration of CoCl42- increase or decrease when the following changes occur?
5. ### math

An initial-value problem is given by the differential equation, f(x,y) = x + y, y(0) = 1.64 The Euler-midpoint method is used to find an approximate value to y(0.1) with a step size of h = 0.1. Then use the integrating factor method, …
6. ### Differential Equations (Another) Cont.

For the following initial value problem: dy/dt=1/((y+1)(t-2)) a)Find a formula for the solution. b) State the domain of definition of the solution. c) Describe what happens to the solution as it approaches the limit of its domain of …
7. ### Differential Equations

For the following initial value problem: dy/dt=1/((y+1)(t-2)), y(0)=0 a)Find a formula for the solution. b) State the domain of definition of the solution. c) Describe what happens to the solution as it approaches the limit of its …
8. ### Math

Consider the initial value problem y'' +5y'+6y=0, y(0)=4.87 and y'(0)=Beta where Beta>0 Determine the coordinates t_m and y_m of the maximum point of the solution as functions of Beta.
9. ### Calculus

Consider f(x)=x^2/(x^2+a), a>0. Determine the effect on the graph of f if a is varied. A. Each y value is multiplied by a B. As a increases, the vertical tangent lines move further from the origin C. The graph of the curve is shifted …
10. ### Math

1. Which function represents an initial population that increases 22% per year where A represents the initial value and X represents time in years?

More Similar Questions