Continuous numerical methods for ODEs with defect control

[1]  Hans J. Stetter Considerations concerning a theory for ode-solvers , 1978 .

[2]  Hans J. Stetter Interpolation and Error Estimation in Adams $PC$-Codes , 1979 .

[3]  G. Wanner,et al.  Perturbed collocation and Runge-Kutta methods , 1981 .

[4]  M. K. Horn,et al.  Fourth- and Fifth-Order, Scaled Rungs–Kutta Algorithms for Treating Dense Output , 1983 .

[5]  L. Shampine Interpolation for Runge–Kutta Methods , 1985 .

[6]  Wayne H. Enright,et al.  Interpolants for Runge-Kutta formulas , 1986, TOMS.

[7]  M. Zennaro Natural continuous extensions of Runge-Kutta methods , 1986 .

[8]  L. S. Baca,et al.  Practical aspects of interpolation in Runge-Kutta codes , 1987 .

[9]  John D. Pryce,et al.  Two FORTRAN packages for assessing initial value methods , 1987, TOMS.

[10]  W. H. Enright,et al.  Effective solution of discontinuous IVPs using a Runge-Kutta formula pair with interpolants , 1988 .

[11]  W. H. Enright Analysis of error control strategies for continuous Runge-Kutta methods , 1989 .

[12]  Desmond J. Higham,et al.  Robust defect control with Runge-Kutta schemes , 1989 .

[13]  W. H. Enright A new error-control for initial value solvers , 1989 .

[14]  Desmond J. Higham Defect estimation in Adams PECE codes , 1989 .

[15]  Desmond J. Higham,et al.  Runge-Kutta Defect Control Using Hermite-Birkhoff Interpolation , 1991, SIAM J. Sci. Comput..

[16]  W. H. Enright,et al.  A Runge-kutta Type Boundary Value Ode Solver with Defect Control , 1993 .

[17]  J. H. Verner,et al.  Differentiable interpolants for high-order Runge-Kutta methods , 1993 .

[18]  W. H. Enright,et al.  The relative efficiency of alternative defect control schemes for high-order continuous Runge-Kutta formulas , 1993 .

[19]  Ronald F. Boisvert,et al.  The Quality of Numerical Software: Assessment and Enhancement , 1996, Quality of Numerical Software.

[20]  Wayne H. Enright,et al.  Runge-Kutta Software with Defect Control for Boundary Value ODEs , 1996, SIAM J. Sci. Comput..

[21]  Wayne H. Enright,et al.  The evaluation of numerical software for delay differential equations , 1996, Quality of Numerical Software.

[22]  W. H. Enright,et al.  Continuous Runge-Kutta methods for neutral Volterra integro-differential equations with delay , 1997 .

[23]  W. H. Enright,et al.  Superconvergent Interpolants for the Collocation Solution of Bvodes , 1997 .

[24]  W. Enright,et al.  Convergence Analysis of the Solution of Retarded and Neutral Delay Differential Equations by Continuous Numerical Methods , 1998 .

[25]  Wayne H. Enright,et al.  Superconvergent Interpolants for the Collocation Solution of Boundary Value Ordinary Differential Equations , 1999, SIAM J. Sci. Comput..

[26]  Wayne H. Enright,et al.  Superconvergent interpolants for collocation methods applied to mixed-order BVODEs , 2000, TOMS.

[27]  Lawrence F. Shampine,et al.  A BVP solver based on residual control and the Maltab PSE , 2001, TOMS.