

numarical Problem 4: Given-(y1),yo)-2 Answer points (19,20,21 and 22). 19) The estimated value of y(3) usng 20) The estimated value of y(3) using Modified 21) The estimated value of y (1) using de...
Question 1: Given the initial-value problem 12-21 0 <1 <1, y(0) = 1, 12+10 with exact solution v(t) = 2t +1 t2 + 1 a. Use Euler's method with h = 0.1 to approximate the solution of y b. Calculate the error bound and compare the actual error at each step to the error bound. c. Use the answers generated in part (a) and linear interpolation to approximate the following values of y, and compare them to the actual value...
(16 pts) Given boundary value problem (1 - 2)y" + 2xy' = 1 y(0) = 0, y'(1) = 0 (a) (6 pts) yı = 1 is a solution to homogeneous equation (1 – 22)y" + 2xy' = 0, find a second solution y2 by reduction of order method. (b) (6 pts) Find Green's function G (1, t) of the BVP. (c) (4 pts) Find a solution of the BVP using G (2,t).
1.) solve the problem y'=(x+1)y yo) =1 numencally for 4 (02) using hol? 2 1:21 A B 1.2 E).221 2.) y - 4y + 4y =0 A. Y = e Y2 = Xe x A Two linearly independent Solutions of the differenthal equation are? B. Y =é 3x Cirl =é D. Yl=eax E, Y = ex 1 Y 2 =Xex + Y2 = Xerzy 42=e-2x Y = e zx + 3.) The radius of convergence of the Power Senes x/n...
Problem Thre: 125 points) Consider the following initial value problem: dy-2y+ t The y(0) -1 ea dt ical solution of the differential equation is: y(O)(2-2t+3e-2+1)y fr exoc the differential equation numerically over the interval 0 s i s 2.0 and a step size h At 0.5.A Apply the following Runge-Kutta methods for each of the step. (show your calculations) i. [0.0 0.5: Euler method ii. [0.5 1.0]: Heun method. ii. [1.0 1.5): Midpoint method. iv. [1.5 2.0): 4h RK method...
Given are five observations for two variables, r and y. 3 4 5 1 2 7 6 11 14 4 The estimated regression equation is y = 1.2 + 2.4r Compute the mean square error using the following equation (to 3 decimals). a. SSE s2=MSE n- 2 decimals). b. Compute the standard error of the estimate using the following equation (to SSE VMSE Vn-2 SE c. Compute the estimated standard deviation bi using the following equation (to 3 decimals). Sp...