33 years of numerical instability, Part I

[1]  L. Trefethen Group velocity in finite difference schemes , 1981 .

[2]  T. Ström On Logarithmic Norms , 1975 .

[3]  C. Desoer,et al.  The measure of a matrix as a tool to analyze computer algorithms for circuit analysis , 1972 .

[4]  Hans J. Stetter,et al.  Stabilizing predictors for weakly unstable correctors , 1965 .

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

[6]  P. Henrici Discrete Variable Methods in Ordinary Differential Equations , 1962 .

[7]  H. Kreiss Über Die Stabilitätsdefinition Für Differenzengleichungen Die Partielle Differentialgleichungen Approximieren , 1962 .

[8]  G. Dahlquist Stability and error bounds in the numerical integration of ordinary differential equations , 1961 .

[9]  W. E. Milne,et al.  Stability of a Numerical Solution of Differential Equations—Part II , 1960, JACM.

[10]  Hans-otto Kreiss Über Matrizen die beschränkte Halbgruppen erzeugen. , 1959 .

[11]  R. R. Reynolds,et al.  Stability of a Numerical Solution of Differential Equations , 1959, JACM.

[12]  川口 光年,et al.  R.D.Richtmyer: Difference Methods for Initial-Value Problems. Interscience Pub. Inc. New York, 1957, xii+238頁, 15×23cm, \2,600. , 1958 .

[13]  R. D. Richtmyer,et al.  Difference methods for initial-value problems , 1959 .

[14]  W. Uhlmann Fehlerabschätzungen bei Anfangswertaufgaben gewöhnlicher Differentialgleichungssysteme 1. Ordnung , 1957 .

[15]  G. Dahlquist Convergence and stability in the numerical integration of ordinary differential equations , 1956 .

[16]  R. D. Richtmyer,et al.  Survey of the stability of linear finite difference equations , 1956 .

[17]  H. Eltermann Fehlerabschätzung bei näherungsweiser Lösung von Systemen von Differentialgleichungen erster Ordnung , 1955 .

[18]  G. Dahlquist Convergence and stability for a hyperbolic difference equation with analytic initial-values , 1954 .

[19]  H. J. Gray,et al.  Numerical methods in digital real-time simulation , 1954 .

[20]  G. Dahlquist On the analytic continuation of Eulerian products , 1952 .

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

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

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

[24]  J.,et al.  Numerical Integration of the Barotropic Vorticity Equation , 1950 .

[25]  George G. O'Brien,et al.  A Study of the Numerical Solution of Partial Differential Equations , 1950 .

[26]  R. D. Richtmyer,et al.  A Method for the Numerical Calculation of Hydrodynamic Shocks , 1950 .

[27]  John Todd,et al.  Solution of Differential Equations by Recurrence Relations , 1950 .

[28]  Pentti Laasonen,et al.  Über eine Methode zur Lösung der Wärmeleitungs-gleichung , 1949 .

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

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

[31]  Lothar Collatz,et al.  Numerische Behandlung von Differentialgleichungen , 1948 .

[32]  A. Turing ROUNDING-OFF ERRORS IN MATRIX PROCESSES , 1948 .

[33]  J. Neumann,et al.  Numerical inverting of matrices of high order , 1947 .

[34]  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.

[35]  H. Hotelling Some New Methods in Matrix Calculation , 1943 .

[36]  R. Zurmühl,et al.  Beiträge zu den Interpolationsverfahren der numerischen Integration von Differentialgleichungen 1. und 2. Ordnung . , 1942 .

[37]  L. Collatz Über das Differenzenverfahren bei Anfangswertproblemen partieller Differentialgleichungen , 1936 .

[38]  R. Courant,et al.  Über die partiellen Differenzengleichungen der mathematischen Physik , 1928 .