Use Euler's modified method to solve the initial value problem dx/dt=(1+x^2)/t,1<=t<=4, x(1)=0

Jaydan Ball

Jaydan Ball

Open question

2022-08-22

I am asked to solve the following problem. Use Euler's modified method to solve the initial value problem d x d t = 1 + x 2 t , 1 t 4 , x ( 1 ) = 0
The step size is not given here. Now, I can solve this using Euler's method but I am not able to find the formula for modified one in the mentioned textbook. So, I need the method here. I need to use the following as textbook: Brain Bradie, A friendly Introduction to Numerical Analysis (Pearson)

Answer & Explanation

Andre Ferguson

Andre Ferguson

Beginner2022-08-23Added 12 answers

You can find the method under the name Heuns's method, also as (explicit) trapezoidal method.
k1=h*f(t,x)
k2=h*f(t+h,x+k1)
y+=0.5*(k1+k2)

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