Stiff differential equations solved by Radau methods

[1]  G. Wanner,et al.  Runge-Kutta methods: some historical notes , 1996 .

[2]  C. Lubich,et al.  Runge-Kutta approximation of quasi-linear parabolic equations , 1995 .

[3]  Kjell Gustafsson,et al.  Control-theoretic techniques for stepsize selection in implicit Runge-Kutta methods , 1991, TOMS.

[4]  Ernst Hairer,et al.  Error of Runge-Kutta methods for stiff problems studied via differential algebraic equations , 1988 .

[5]  L. Petzold Order results for implicit Runge-Kutta methods applied to differential/algebraic systems , 1986 .

[6]  Christoph W. Ueberhuber,et al.  Order Results for Implicit Runge–Kutta Methods Applied to Stiff Systems , 1985 .

[7]  P. Deuflhard Order and stepsize control in extrapolation methods , 1983 .

[8]  Christoph W. Ueberhuber,et al.  The Concept of B-Convergence , 1981 .

[9]  Kevin Burrage,et al.  An implementation of singly-implicit Runge-Kutta methods , 1980 .

[10]  E. Hairer,et al.  Order stars and stability theorems , 1978 .

[11]  Theodore A. Bickart,et al.  An Efficient Solution Process for Implicit Runge–Kutta Methods , 1977 .

[12]  John C. Butcher,et al.  On the implementation of implicit Runge-Kutta methods , 1976 .

[13]  Gerhard Wanner,et al.  A short proof on nonlinearA-stability , 1976 .

[14]  John C. Butcher,et al.  A stability property of implicit Runge-Kutta methods , 1975 .

[15]  T. E. Hull,et al.  Comparing numerical methods for stiff systems of O.D.E:s , 1975 .

[16]  B. L. Ehle A-Stable Methods and Padé Approximations to the Exponential , 1973 .

[17]  B. Hulme Discrete Galerkin and related one-step methods for ordinary differential equations , 1972 .

[18]  K. Wright,et al.  Some relationships between implicit Runge-Kutta, collocation and Lanczosτ methods, and their stability properties , 1970 .

[19]  Ralph A. Willoughby,et al.  EFFICIENT INTEGRATION METHODS FOR STIFF SYSTEMS OF ORDINARY DIFFERENTIAL EQUATIONS , 1970 .

[20]  Owe Axelsson,et al.  A class ofA-stable methods , 1969 .

[21]  Richard S. Varga,et al.  DISCRETIZATION ERRORS FOR WELL-SET CAUCHY PROBLEMS.I., , 1965 .

[22]  J. Butcher Integration processes based on Radau quadrature formulas , 1964 .

[23]  G. Dahlquist A special stability problem for linear multistep methods , 1963 .

[24]  P. Hammer,et al.  Trapezoidal methods of approximating solutions of differential equations , 1955 .

[25]  C F Curtiss,et al.  Integration of Stiff Equations. , 1952, Proceedings of the National Academy of Sciences of the United States of America.

[26]  L. Fox,et al.  Some new methods for the numerical integration of ordinary differential equations , 1949, Mathematical Proceedings of the Cambridge Philosophical Society.

[27]  W. Loud On the Long‐Run Error in the Numerical Solution of Certain Differential Equations , 1949 .

[28]  J. Crank,et al.  A practical method for numerical evaluation of solutions of partial differential equations of the heat-conduction type , 1947, Mathematical Proceedings of the Cambridge Philosophical Society.

[29]  Ernst Hairer,et al.  The numerical solution of differential-algebraic systems by Runge-Kutta methods , 1989 .

[30]  G. Dahlquist Error analysis for a class of methods for stiff non-linear initial value problems , 1976 .

[31]  A. Prothero,et al.  On the stability and accuracy of one-step methods for solving stiff systems of ordinary differential equations , 1974 .

[32]  A. Guillou,et al.  La résolution numérique des problèmes différentiels aux conditions initiales par des méthodes de collocation , 1969 .

[33]  J. Butcher Implicit Runge-Kutta processes , 1964 .

[34]  Heinz Rutishauser,et al.  Über die Instabilität von Methoden zur Integration gewöhnlicher Differentialgleichungen , 1952 .

[35]  Germund Dahlquist Fehlerabschätzungen bei Differenzenmethoden zur numerischen Integration gewöhnlicher Differentialgleichungen , 1951 .

[36]  R. Radau Étude sur les formules d'approximation qui servent à calculer la valeur numérique d'une intégrale définie. , 1880 .