C. W. Gear
- 1 ~ETTIS, 1).~. Efficient embedded l~unge-l~utta methods In ~vumencat "l"reatment of LP$llerentml Equatmns, vol. 631, R. Burlirsch, R.D. Grigoneff, and J. Schroder, Eds., Lecture Notes in Mathematms, Sprmger-Verlag, New York, 1976.Google Scholar
- 2 BUTCHER, J.C. Implicit Runge-Kutta processes Math. Comput. 18 {1964), 50-64.Google Scholar
- 3 CAttvzR, M.B. Efficient handhng of discontinuities and time delays in orchnary dlfferenUal equations. In Proc Simulation '77 Symp., Montreux, Switzerland, M. Hamza, Ed., Acta Press, Zurich, SwitzerlandGoogle Scholar
- 4 E~LE, B.L. A-stable methods and Pade approximations to the exponential. SIAM J. Math. Anal. 4 (1973), 671-680Google Scholar
- 5 FEHLBER6, E. Klassiche Runge-Kutta Formeln vierter und medrigerer Ordnung mit Schrittwelten-Kontrolle und im'e Anwendung auf Warmeleltungsprobleme. Computing 6 {1970}, 61-71.Google Scholar
- 6 GEAR, C W. DIFSUB for the solution of ordinary dlfferenhal equations. Commun. ACM 14, 3 (March 1971), 185-190. Google Scholar
- 7 GEAR, C W. Rational approximations by imphclt Runge-Kutta schemes. BIT 10 (1970), 20-22.Google Scholar
- 8 GEAR C.W Runge-Kutta starters for mulhstep methods. Rep. 78-938, Dept. Comput. Scl., Univ. Illinois, Urbana, 1978.Google Scholar
- 9 HINDMARSH A.C. GEAR: Ordinary differential equation solver Rep. UCID-30001, Rev. 3, Lawrence Livermore Lab., Llvermore, Cahf., 1974.Google Scholar
- 10 HULL, T.E., ENRIGHT, W.H., FELLEN, B.M., AND SEDGWICK, A.E. Comparing numerical methods for ordinary differential equations. SIAM J. Numer. Anal. 9 (1972), 603-637.Google Scholar
- 11 KaOGH, F T VODQ/SVDQ/DVDQ--Varlable order integrators for the numerical solution of ordinary differential equations. Sec. 314, Subroutine Write-up, Jet Propulsion Lab., Pasadena, Calif., 1969Google Scholar
- 12 NORDSIECK, A. On the numerical mtegraUon of ordinary differential equations. Math. Comput. 16 (1962), 22-49.Google Scholar
- 13 SV~AMPINZ, L.F., AND GORDON, M.K. Computer Solutmn of Ordinary Differential Equatmns: The In~tml Value Problem. Freeman, San Francisco, 1975.Google Scholar
- 14 STETTER, H.J. Analysts of D~scret~zatmn Methods for Ordinary D~fferent~al Equations, vol 23, Sprmger Tracts in Natural Philosophy, Sprmger-Verlag, New York, 1973.Google Scholar
- 15 STETTER, H.J Asymptotm expansions for the error of chscretizatlon algorithms for nonhnear functional equations. Numer. Math. 7 (1965), 18-31Google Scholar
Index Terms
- Runge-Kutta Starters for Multistep Methods
Recommendations
Strong stability of singly-diagonally-implicit Runge--Kutta methods
This paper deals with the numerical solution of initial value problems, for systems of ordinary differential equations, by Runge-Kutta methods (RKMs) with special nonlinear stability properties indicated by the terms total-variation-diminishing (TVD), ...
Multistep Runge–Kutta methods for Volterra integro-differential equations
AbstractIn this paper, we investigate multistep Runge–Kutta methods for Volterra integro-differential equations. First, we derive order conditions for methods of order p and stage order q = p − 1 for p ⩽ 4. Then, stability properties of these ...
High Order Multisymplectic Runge--Kutta Methods
† Special Section on Two Themes: Planet Earth and Big DataWe study the spatial semidiscretizations obtained by applying Runge--Kutta (RK) and partitioned Runge--Kutta (PRK) methods to multisymplectic Hamiltonian PDEs. These methods can be regarded as multisymplectic $hp$-finite element methods for wave equations. ...
Comments