Consider the initial value problem 𝑑𝑦 𝑑𝑥 = 𝑥 − 𝑦2 , 𝑦(0) = 1 (2)
Posted: Thu May 12, 2022 12:42 pm
Consider the initial value problem
𝑑𝑦
𝑑𝑥
= 𝑥 − 𝑦2
, 𝑦(0) = 1 (2)
(a) Use the modified Euler method with step h = 0.1 to determine the approximate value
of the solution at x = 0.1. Give the answer correct to the fourth decimal place.
(b) Use the fourth order Runge-Kutta method with step h = 0.5 to determine the
approximate value of the solution at x = 0.5. Give the answer correct to the fourth
decimal place
3. (3+6=9 marks) Consider the initial value problem = x - y2 y(0) = 1 (2) ) (a) Use the modified Euler method with step h - 0.1 to determine the approximate value of the solution at x = 0.1. Give the answer correct to the fourth decimal place. (b) Use the fourth order Runge-Kutta method with step h - 0.5 to determine the approximate value of the solution at x = 0.5. Give the answer correct to the fourth decimal place
𝑑𝑦
𝑑𝑥
= 𝑥 − 𝑦2
, 𝑦(0) = 1 (2)
(a) Use the modified Euler method with step h = 0.1 to determine the approximate value
of the solution at x = 0.1. Give the answer correct to the fourth decimal place.
(b) Use the fourth order Runge-Kutta method with step h = 0.5 to determine the
approximate value of the solution at x = 0.5. Give the answer correct to the fourth
decimal place
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