Solving ordinary differential equations I (2nd revised. ed.): nonstiff problems
Solving ordinary differential equations I (2nd revised. ed.): nonstiff problems
Selected papers of the sixth conference on Numerical Treatment of Differential Equations
Semidiscretization in time of nonlinear parabolic equations with blowup of the solution
SIAM Journal on Numerical Analysis
Journal of Computational and Applied Mathematics - Special issue: nonlinear problems with blow-up solutions: applications and numerical analysis
Frequency determination and step-length control for exponentially-fitted Runge---Kutta methods
Journal of Computational and Applied Mathematics
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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 驴 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.