Answer to Question #309937 in Quantitative Methods for Raaa

Question

Use Euler and modified Euler method with one step find the value of y at x=0.1 for given dy/dx=x^2 +y and y=0.94 when x=0

Answer 1

f(x, y) = x² + y; x₀=0; y₀=0.94; h=0.1 The task is to find y₁=y(x₁), where x₁=x₀+h

1 Euler method:

y₁ = y₀ + h f(x₀, y₀) = 0.94 + 0.1 (0² + 0.94) = 1.034

2 Modified Euler method:

y_1/2 = y₀ + h/2 f(x₀, y₀) = 0.94 + 0.05 (0² + 0.94) = 0.987

x_1/2 = x₀ + h/2 = 0 + 0.05 = 0.05

y₁ = y₀ + h f(x_1/2, y_1/2) = 0.94 + 0.1 (0.05² + 0.987) = 1.03895