Composed BDF schemes with complex coefficients increase order by one, supply order p+1 error estimates from the imaginary part, break the Dahlquist barrier up to order 8, and give step-ratio stability bounds for non-uniform meshes.
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Error estimation for numerical approximations of ODEs via composition techniques. Part II: BDF methods
Composed BDF schemes with complex coefficients increase order by one, supply order p+1 error estimates from the imaginary part, break the Dahlquist barrier up to order 8, and give step-ratio stability bounds for non-uniform meshes.