Question

What are the conditions on the parameters for linear multistep methods so that the methods are regular? Would appreciate a detailed explanation.

Answer 1

Well it is to inform you that Linear multistep methods are used for the numerical problems of ODE's. Conceptually, a numerical method starts from an initial point and then takes a shortly forward in time to find the next solution point. The process continues with subsequent steps to map out the solution.

Linear multistep methods mostly use for ODE/ IVP

Numerical solution of ODE's, A prior error estimates of LMM, Linear multistep methods with region of absolute stability and uniform boundedness of powers of Frobenius matrices.

System of ODEs u'(t) = F(t,u(t)), t > 0, u(0) = u0

The linear multi (k) step method