Keywords
- Collocation Method
- Implicit Euler Method
- Collocation Solution
- Collocation Scheme
- Collocation Node
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References
O. Axelsson A Class of A-stable Methods BIT Vol. 9 (1969), pp. 185–199
F.H. Chipmann Numerical Solution of Initial Value Problems using A-stable Runge-Kutta Processes Dept. of A.A.C.S, Univ. of Waterloo, Research Report, CSSR 2042, 1971
C. de Boor, B. Swartz Collocation at Gaussian Points SIAM J. Num. Anal. Vol. 10(1973), pp. 582–606
B.L. Ehle On Padé Approximations to the Exponential Function and A-stable Methods for the Numerical Solution of Initial Value Problems Dept. of A.A.C.S., Univ. of Waterloo Research Report, CSSR 2010, 1969
R. Frank, C.W. Ueberhuber Iterated Defect Correction for Runge-Kutta Methods Report Nr. 14/76, Inst. f. Num. Math. Technical University of Vienna
R. Frank, C.W. Ueberhuber Iterated Defect Correction for the Efficient Solution of Stiff Systems of Ordinary Differential Equations Report Nr. 17/76, Inst. f. Num. Math. Technical University of Vienna
R. Frank, J. Hertling, C.W. Ueberhuber Iterated Defect Correction based on Estimates of the Local Discretization Error Report Nr. 18/76, Inst. f. Num. Math. Technical University of Vienna
V.L. Pereyra On Improving an Approximate Solution of a Functional Equation by Deferred Corrections Num. Math. Vol. 8 (1966), pp. 376–391
R.D. Russel, L.F. Shampine A Collocation Method for Boundary Value Problems Num. Math. Vol. 19 (1972), pp. 1–28
H.J. Stetter Economical Global Error Estimation, in R.A. Willoughby (Ed.) Stiff Differential Systems Plenum Press, New York-London, 1974, pp. 245–258
R. Weiss The Application of Implicit Runge-Kutta and Collocation Methods to Boundary Value Problems Math. Comp. Vol. 28 (1974), pp. 449–464
K. Wright Some Relationships between Implicit Runge-Kutta, Collocation and Lanczos τ Methods, and their Stability Properties BIT Vol. 10 (1970), pp. 217–227
P.E. Zadunaisky A Method for the Estimation of Errors Propagated in the Numerical Solution of a System of Ordinary Differential Equations, in Proc. Intern. Astron. Union Symposium No. 25, Thessaloniki 1964 Academic Press, New York, 1966
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Frank, R., Ueberhuber, C.W. (1978). Collocation and iterated defect correction. In: Bulirsch, R., Grigorieff, R.D., Schröder, J. (eds) Numerical Treatment of Differential Equations. Lecture Notes in Mathematics, vol 631. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0067461
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DOI: https://doi.org/10.1007/BFb0067461
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