In Numerical Ordinary Differential Equations the amplificati

In Numerical Ordinary Differential Equations the amplification factor is Gi = absolute value of (Yi+1)/(Yi) = absolute value of (1-hlambda). What condition guarantees the stability of a numerical method?

Solution

In order for the stability of numerical method, the absolute value Gi which is |y(i+1)/yi| must be less than 1

Otherwise the system won\'t be stable and the system series will approach to infinity with the increase in value of n

Other stability condition is that lambda must be greater than zero, since the value of h will be always positive and we want the modulus value or absolute value of (1-hlambda) must be less than 1