Variable-Coefficient Difference Schemes for Quasilinear Evolution Problems
We review several integration methods leading to variable- coefficient schemes and/or to exact schemes for ODEs (functional fitting; Principle of Coherence). Conditions for obtaining coefficients that are independent of the time t and of the time step τ are investigated. It is shown that some of the discussed schemes lead to efficient difference schemes for problems from applications, in particular for highly oscillatory ODEs and for parabolic equations with blow-up solutions.
KeywordsCollocation Method Trapezoidal Rule Error Expansion Apparent Singularity Collocation Scheme
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