Exam 8: Numerical Methods

Consider the initial value problem This question is related to using the fourth-order backward differentiation formula to estimate the solution y(0.2) using a step size of h =0.05 . For the following problem, you will need these values to carry out the computation: Which of the following expressions represents the error incurred in using this method to estimate y(0.2)?

Consider the initial value problem This question is related to using the predictor-corrector method to estimate the solution y(0.2) using a step size of h = 0.05. For this problem, you will need these values to carry out the computations: To use the corrector formula, you need . Which of the following is the correct expression for ?

Consider the initial value problem This question is related to using the predictor-corrector method to estimate the solution y(0.2) using a step size of h = 0.05. For this problem, you will need these values to carry out the computations: To use the corrector formula, you need f₄ . Which of the following is the correct expression for f₄

The velocity (measured in meters per second) of an air-dropped container of food and supplies affixed to a parachute is described by the function v(t) = 56 tanh(0.23t), t $\ge$ 3.2, where t is measured in seconds. You are interested in approximating the vertical distance s(t) traveled by the package by time t = 3.45 seconds.Using a step size of h = 0.25 seconds, compute the vertical distance traveled in the first 3.45 seconds.

The velocity (measured in meters per second) of an air-dropped container of food and supplies affixed to a parachute is described by the function v(t) = 66.8 tanh(0.20t), t $\ge$ 2.4, where t is measured in seconds. You are interested in approximating the vertical distance s(t) traveled by the package by time t = 2.50 seconds.Using a step size of h = 0.10 seconds, compute the vertical distance traveled in the first 2.50 seconds. K1= ________

Consider the following initial value problem The following question pertains to the various computational steps and identifications involved in applying Runge-Kutta's 4th order method to evaluate y(0.15). To compute identify the parameter below. In what follows, K₂ = ________

Consider the initial value problem This question is related to using the fourth-order backward differentiation formula to estimate the solution y(0.2) using a step size of . For the following problem, you will need these values to carry out the computation: Which of the following is the value of

Consider the initial value problem This question is related to using the predictor-corrector method to estimate the solution y(0.2) using a step size of h = 0.05. Which of the following is the correct formula for

Consider the system of initial value problems given by This problem can be expressed using matrix notation as When using the Euler method with h = 0.05, how many iterations n do you need in order to estimate the solution at t = 2 × 0.05? n = _______

Consider the following initial value problem The following question pertains to the various computational steps and identifications involved in applying Runge-Kutta's 4th order method to evaluate y(0.7). To compute , identify the parameter below. In what follows K₄ = ________

Consider the initial value problem This question is related to using the predictor-corrector method to estimate the solution y(0.2) using a step size of h = 0.05. For this problem, you will need these values to carry out the computations: Which of the following show a portion of the formula for the corrected value of

Consider the initial value problem This question relates to using The Euler method to approximate the solution of this problem at t = 0.4 using a step size of h = Which of the following identifications are correct when setting up Euler's method Select all that apply.

Consider the initial value problem This question is related to using the predictor-corrector method to estimate the solution y(0.2) using a step size of h = 0.05. For this problem, you will need these values to carry out the computations: Which of the following is the predicted value for

Consider the initial value problem Use the Runge-Kutta method to approximate the solution at using a step size of h = 0.12. (a) Find the following constants needed for the Runge-Kutta method. (i) K ₁= ________ (ii) K ₂= ________ (iii) K ₃= ________

Consider the initial value problem This question is related to using the predictor-corrector method to estimate the solution y(0.2) using a step size of h = 0.05. For this problem, you will need these values to carry out the computations: Which of the following is the correct formula for

Consider the system of initial value problems given by This problem can be expressed using matrix notation as Where What are the values of when using the improved Euler method with h = 0.05?

Consider the initial value problem This question relates to using the Euler method to approximate the solution of this problem at t = 0.1 using a step size of h = Which of the following equals

Given the initial value problem how many steps n are needed for the RK method to find an approximation for y(1.8) using a step size of h = 0.010? N = ________

Consider the initial value problem This question is related to using the fourth-order backward differentiation formula to estimate the solution y(0.2) using a step size of h= 0.05 Which of these is the correct formula for

Consider the initial value problem This question is related to using the Runge-Kutta method for approximating the solution y at t= 1.1 with a step size of h = 0.05. To find Y₁, first calculate the following in order to apply the Runge-Kutta method. Express your answers accurate to seven decimal places. (i) K₁ = ________ (ii) K₂ = ________ (iii) K₃ = ________ (iv) K₄= ________ (v) So, using the Runge-Kutta method, Y₁ = ________