[MATLAB] Euler_method

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목차

Introduce the problem
Solve the problem by Analytic method
Solve the problem by Euler’s method
Discussion of result

본문내용

1.Introduce the problem
Use Euler’s method with step size h=0.1 to approximate the solution to the initial value problem

y’=x √y, y(1)=4

at the point x=1.1, 1.2, 1.3, 1.4 and 1.5. Compare your numerical result with the exact solution.

2.Solve the problem by Analytic method
y’=x √y, y(1)=4

→ dy/dx= x √y
→ 1/ √y ⋅dy=x⋅dx
→ ∫1/ √y ⋅dy=∫x⋅dx
→ 2 √y =1/2⋅x²+C
→ 4=1/2+C
(∵y(1)=4)

∴C=7/2

참고 자료

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