With the method of RK of order FOUR determine the approximate solution of the ODE: dy dt 4e0.8t - 0.5y Wearing h = 0.5 with y(0) = 2, from t=0 to t=4. Write an algorithm and its implementation in the Octave program.
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- 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)=0.5find a bound for the number of iterations needed to achieve an approximation with accuracy 10−3 to the solution of 2x 6 − 5x 4 + 2 = 0 in the interval [0, 1] while using the bisection methodIn an experiment on the effect of caffeine on time to complete a manual task, Dr. Ruybal had three treatment levels: 0 mg of caffeine, 150 mg of caffeine, and 300 mg of caffeine. She assigned an equal number of participants to each of his 3 conditions (N = 39). He calculated his ΣX2tot = 95, ΣXtot = 50, and this partial computation of the SSbn formula: = 70. Plug this into the complete formula and compute the rest for SSbn. Label your answers. A. What is SSbn? B. What is SSwn? C. What is MSbn? D. What is MSwn? E. What is Fobt ? F. Use alpha = .05. What is Fcrit ? AND What should she conclude about the statistical hypothesis? H. Should post-hoc paired comparisons be conducted? Why or why not?
- SHOW ONLY THE FORMULA TO GET THE ITERATIONS IN EXCEL USING THE METHOD GIVENcarry 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. 16.y′=0.5−t+2y,y(0)=1Calculate 3 iterations of the Bisection Method to find the Zero of the function "e^x-2" in I = [0, 1]. How many iterarions would be necessary to find an aproach of this Zero with precision ∈ = 10^-513??
- Find the coefficient of X^35 in the generating function (x^4+x^5+x^6+x^7+x^8)^5 (Show work and leave final answer in C(n,r) form.)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.Prior to entering in the corresponding input fields, all numerical answers should be rounded to 6-digit floating-point numbers. Given a real number z, the symbol z˜ denotes the result of rounding of z to a 6-digit floating-point number. i)use the Bisection method to find an approximation pN of the unique solution p the equation 3.60x(1-x2+x)In(x)=x2-1 in[a,b]=[0.05,0.5] such that RE(p˜N≈p˜N-1)<10-3.