Titlebook: Numerical Methods for Ordinary Differential Equations; Initial Value Proble David F. Griffiths,Desmond J. Higham Textbook 2010 Springer-Ver

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,Linear Multistep Methods—IV: Systems of ODEs,In this chapter we describe the use of LMMs to solve systems of ODEs and show how the notion of absolute stability can be generalized to such problems. We begin with an example.

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,Linear Multistep Methods—V: Solving Implicit Methods,The discussion of absolute stability in previous chapters shows that it can be advantageous to use an implicit LMM—usually when the step size in an explicit method has to be chosen on grounds of stability rather than accuracy. One then has to compute the numerical solution at each step by solving a nonlinear system of algebraic equations.

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,Runge-Kutta Methods–II Absolute Stability,The notion of absolute stability developed in Chapter 6 for LMMs is equally relevant to RK methods. Applying an RK method to the linear ODE .′(.) = λ.(.) with ℜ(λ) < 0, absolute stability requires that .. → 0 as . → ∞.

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Numerical Methods for Ordinary Differential EquationsInitial Value Proble