FM - Further Pure 1 - 8) Numerical methods

Question 1

Formula for the first-order differential equation

Answer 1

y_n+1 = y_n + h(dy/dx)_n

Question 2

Formula for the midpoint method of the first-order differential equation

Answer 2

y_n+1 = y_n-1 + 2h(dy/dx)_n

Question 3

Formula for the second-order differential equation

Answer 3

y_n+1 = 2y_n - y_n-1 + h²(d²y/dx²)_n