2 Three step Adams Bashforth method Consider the

Last updated: 10/22/2023

2 Three step Adams Bashforth method Consider the interpolation nodes t 2 1 t where t t j jh a Write down the Lagrange interpolation polynomial P t for the function f t y t at the nodes above b Consider the IVP y t f t y t integrate the Lagrange polynomial P t from a exactly to determine bi b and b3 such that Yi 1 yih b f ti Yi b f ti 1 Yi 1 b3f t 2 2 As usual y denotes the value of y t at t tk Your answers b should be given as fractions Hint you may note for b we have f L t dt 2h evaluate the integral and do the same for b2 b hb pti 1 S t ti 1 t t 2 dt