(Solved):
Which of these multistep methods is convergent? a. xnxn2=h(fn3fn1+4fn2 ...
Which of these multistep methods is convergent? a. xn??xn?2?=h(fn??3fn?1?+4fn?2?) b. xn??2xn?1?+xn?2?=h(fn??fn?1?) c. xn??xn?1??xn?2?=h(fn??fn?1?) d. xn??3xn?1?+2xn?2?=h(fn?+fn?1?) e. xn??xn?2?=h(fn??3fn?1?+2fn?2?)
To determine the convergence of the given multistep methods, we can use the concept of consistency and stability. A multistep method is said to be consistent if the local truncation error tends to zero as the step size h tends to zero. A method is stable if the errors in the solution remain bounded as h tends to zero.