Recursive collocation for the numerical solution of stiff ordinary differential equations
Math. Comp. 28 (1974), 475-481
Full-text PDF Free Access
Similar Articles |
Abstract: The exact solution of a given stiff system of nonlinear (homogeneous) ordinary differential equations on a given interval I is approximated, on each subinterval corresponding to a partition of I, by a linear combination of exponential functions. The function will involve only the "significant" eigenvalues (in a sense to be made precise) of the approximate Jacobian for . The unknown vectors in are computed recursively by requiring that satisfy the given system at certain suitable points in (collocation), with the additional condition that the collection of these functions represent a continuous function on I satisfying the given initial conditions.
G. Bjurel et al., Survey of Stiff Ordinary Differential Equations, Report NA 70.11, Dept. of Computer Science, Royal Institute of Technology, Stockholm, 1970.
W. Gear, The automatic integration of stiff ordinary differential
equations., Information Processing 68 (Proc. IFIP Congress, Edinburgh,
1968) North-Holland, Amsterdam, 1969, pp. 187–193. MR 0260180
Hahn, Stability of motion, Translated from the German
manuscript by Arne P. Baartz. Die Grundlehren der mathematischen
Wissenschaften, Band 138, Springer-Verlag New York, Inc., New York, 1967.
0223668 (36 #6716)
D. Lambert, Computational methods in ordinary differential
equations, John Wiley & Sons, London-New York-Sydney, 1973.
Introductory Mathematics for Scientists and Engineers. MR 0423815
Liniger and Ralph
A. Willoughby, Efficient integration methods for stiff systems of
ordinary differential equations, SIAM J. Numer. Anal.
7 (1970), 47–66. MR 0260181
- G. Bjurel et al., Survey of Stiff Ordinary Differential Equations, Report NA 70.11, Dept. of Computer Science, Royal Institute of Technology, Stockholm, 1970.
- C. W. Gear, "The automatic integration of stiff ordinary differential equations (with discussion)," Information Processing 68 (Proc. IFIP Congress, Edinburgh, 1968), North-Holland, Amsterdam, 1969, pp. 187-193. MR 41 #4808. MR 0260180 (41:4808)
- W. Hahn, Stability of Motion, Translated from the German Manuscript, Die Grundlehren der math. Wissenschaften, Band 138, Springer-Verlag, New York, 1967. MR 36 #6716. MR 0223668 (36:6716)
- J. D. Lambert, Computational Methods in Ordinary Differential Equations, Wiley, London, 1973. MR 0423815 (54:11789)
- W. Liniger & R. A. Willoughby, "Efficient integration methods for stiff systems of ordinary differential equatons," SIAM J. Numer. Anal., v. 7, 1970, pp. 47-66. MR41 #4809. MR 0260181 (41:4809)
Retrieve articles in Mathematics of Computation
Retrieve articles in all journals
System of stiff nonlinear homogeneous ordinary differential equations,
approximate solution by sums of exponential functions,
© Copyright 1974 American Mathematical Society