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You are given the differential equation dy/dx = y' = f(x, y) with initial condition y(0 ) 1 = . The following numerical method is also given:
where fn = f( xn , yn) = f(nh, yn) x , y f nh, y = = and h is the integration step.
(a) Is this an explicit or implicit method? Explain you answer.
(b) Find an expression for local error of this method.
(c) If one takes f = - σy (where σ > 0 and constant) is this method stable? Prove your answer mathematically.
(d) What is the condition for the iterative convergence of the method (when f = - σy )? Show that fulfillment of the condition for stability of the method assures iterative convergence.
Explain what central tendency and variability are. In your answer define what the mean, median, mode, variance, and standard deviation are. What is the difference between the descr
calcation
Mid year population 440000 Late fatal death 29 No. of live birth 5200 No. of infant death 423 No. of maternal death 89 No. of infant deaths i
Show that the ISB in a bin containing the origin of the double exponen-tial density, f(x) = exp(-|x|)/2, is O(h 3 ); hence, the discontinuity in the derivative of f does not have a
In recent years a number of calculators are available for doing statistical calculations over and above the usual addition, subtraction, multiplication and division. The fx-82 mode
We are interested in assessing the effects of temperature (low, medium, and high) and technical configuration on the amount of waste output for a manufacturing plant. Suppose that
Explain the characteristics of business forecasting.
Let X, Y, and Z refer to the three random variables. It is known that Var(X) = 4, Var(Y) = 9, and Var(Z) = 16. It is further known that E(X) = 1, E(Y) = 2, and E(Z) = 4. Furthermor
Replacement times for CD players are normally distributed with a mean of 7.1 years and standard deviation of 1.4years. Find the probability that a randomly selected CD player will
Canonical correlation analysis (CC) allows the investigation of the relationship between two ,sets of variables. For example, a sociologist may want to investigate the Relationship
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