Question

Vrite down the specific iteration vi-i v t hf tC u) for Fuler's method applied to this problem, and identify the values of to and o (b) Using the step-size h 0.1, compute the approximations yi, /2, vs. (c) Solve the IVP analytically to find the solution y- y(t). Using the results from (b) and (c), tabulate the errorse)vi for k 1,2,3

Answer 1

y' = f(t, y) = ty y(0) = 1. t_0 = 0, y_0 = 1 h = 0.1 Formula: y_k + 1 = y_k + h f(t_k, y_k) & t_k + 1 = t_k + h a^st iteration: y_1 = y_0 + h f(t_0, y_0) = 1 + 0.1 (0 times 1) = 1 Therefore y_1 = 1 t_1 = t_0 + h Therefore t_1 = 0.1 t_1 = 0.1 y_1 = 1 2^nd iteration: y_2 = y_1 + h f(t_1, y_1) = 1 + 0.1 (0.1 times 1) y_2 = 1.01 & t_2 = t_1 + h = 0.2 t_2 = 0.2 y_2 = 1.01 3^rd iteration: y_3 = y_2 + h f(x_2, y_2) = 1.01 + 0.1(0.2 times 1) = 1.01 + 0.02 = 1.03 y_3 = 1.03 t_3 = 0.3 iteration t_k y_k 0 0 1 1 0.1 1 2 0.2 1.01 3 0.3 1.03