Convergence Analysis of Block Implicit One-Step Methods for Solving Differential/Algebraic Equations
Iris Mack · DSpace@MIT (Massachusetts Institute of Technology) · 2011
We will prove that numerical approximants, generated by fixed- stepsize, fixed-formula (FSFF) block implicit one-step methods, applied to smooth, nonlinear, decoupled systems of differential/algebraic equations converge to the true analytic solution.Key Words: fixed-stepsize.fixed-formula block implicit one-step methods, Bansch space, Frechet derivative, Kronecker product notation.consistent.In section four we wil] prove that our FSFF block inriplicit methods are stable.Finally, in section five we will use the fact that consistency and stability imply convergence.I-_ -,- :=i *'i H n: = .1,2, 1 1 di Therefore, equsticns (1.4} can be CDnclsely vvritten 2S -1 Assuming thit *^e;;i£ts, Vve will further simplify system (1.5; tc oDtam Sir,, = hEZrn * iyk * 'll^t- ( 1 r such that.