Use the Euler algorithm with a step size h = 0.2 to find an approximate value of y₁0 for the linear first order initial value problem dy dx in the interval 0 ≤ x ≤ 2 in four decimal places. = sin x - y with y(0) = 1
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Use the Euler algorithm with a step size h = 0.2 to find an approximate value of y10 for the linear first order initial value problem
dy/dx = sinx - y with y(0)=1
in the interval 0 ≤ x ≤ 2 in four decimal places.
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- Use the Euler algorithm with a step size h = 0.2 to find an approximate value of y10 for the linear first-order initial value problem in the interval 0 ≤ x ≤ 2 in four decimal places.Suppose that a numerical method is used to approximate the solution of an initial -value problem over the time inteval [1,5] with 800 uniform time steps. About how many uniform time steps are needed to reduce the global error by a factor of 1/256? a) Runge Kutta method b) Runge- mid point method c) Euler methodBy employing the Adams Fourth-Order Predictor-Corrector algorithm with the step size h=0.2, find the numerical solution of the following problem at t = 0.4; y^ prime =t^ 2 -2e^ -2t; y(0) = 1 , The true solution of this problem is 0 <= t <= 1 , y(t) = (t ^ 3)/3 + e ^ (- 2t) * C * o * m * p * c numerical result with the actual solution at this point. the obtained
- Find the fourth iteration value of z using the Gauss-Seidel method with an initial guess of (1, 1, 3). Round off your final answer to nine decimal places. Do not round off in preliminary calculations.use the cauchy euler method with h=1/m (m integer) to approximate y(3) for the IVP below. ın each case let h-0 (m- inf) and compare the lımıts with the exact values y'=y^2 y(-1)=0Find the third iteration value of z using the Gauss-Seidel method with an initial guess of (1, 1, 2). Round off your final answer to nine decimal places. Do not round off in preliminary calculations.
- a. Use the 2nd-order Runge-Kutta Method to approximate y(t) with h= 0.25 b. Use the 4th-order Runge-Kutta Method to approximate y(t) with h=0.25 c. Plot both sets {yi} obtained in (1) and (2) d. Determine the eventual population level (as t→∞) reached from initial population.Consider the IVP. Apply Euler’s method with the step size h = 1 to this IVP and find the approximate values y1* and y2* of y(2) and y(3), respectively.carry out one step of the Euler method and of the improved Euler method, using the step size h = 0.1. Suppose that a local truncation error no greater than ϵ = 0.0025 is required. Estimate the step size that is needed for the Euler method to satisfy this requirement at the first step.19.y′=(y2+2ty)/(3+t2),y(0)=0.5
- carry out one step of the Euler method and of the improved Euler method, using the step size h = 0.1. Suppose that a local truncation error no greater than ϵ = 0.0025 is required. Estimate the step size that is needed for the Euler method to satisfy this requirement at the first step. 18.y′=√t+y,y(0)=3We want to find the number of ways in which 3r balls can be selected from 2r red ballsand 2r blue balls. Find the generating function corresponding to the above problem in closed form.Consider the following configuration of solar photovoltaic arrays consisting of crystalline silicon solar cells. There are two subsystems connected in parallel, each one containing two cells. In order for the system to function, at least one of the two parallel subsystems must work. Within each subsystem, the two cells are connected in series, so a subsystem will work only if all cells in the subsystem work. Consider a particular lifetime value t0, and suppose we want to determine the probability that the system lifetime exceeds t0.Let Ai denote the event that the lifetime of cell i exceeds t0(i = 1, 2, , 4). We assume that the Ai's are independent events (whether any particular cell lasts more than t0 hours has no bearing on whether or not any other cell does) and that P(Ai) = 0.6 for every i since the cells are identical. Using P(Ai) = 0.6, the probability that system lifetime exceeds t0 is easily seen to be 0.5904. To what value would 0.6 have to be changed in order to increase…