Answer to Question #158749 in Quantitative Methods for manish

Question

Given dy/dx = y-x,where y(0) = 2, find y(0.1) and y(0.2) by Euler’s method up to two decimal places.

Answer 1

Solution

Euler method is a numerical procedure for solving ordinary differential equations with a given initial value.

For

y’(x) = f(x,y(x)), y(x₀)=y₀ 

the size of every step h and x_n = x₀+n*h an approximation of the solution to the ODE is

y_n+1 = y_n + h*f(x_n,y_n)  

In this case x₀ = 0, y₀ = 2, f(x,y) = y – x, h = 0.1

So

y_n+1 = y_n + h*(y_n – x_n ) = (1 + h)*y_n – h*x_n  

y₁ = y(0.1) = 2.2,  y₂ = y(0.2) = 2.41

Answer

y(0.1) = 2.2,  y(0.2) = 2.41