Abstract:A first order method is presented for solution of the initial-value problem for a differential equation of neutral type with implicit delay in the critical case where the time-lag is zero and the method of stepwise integration does not apply. A convergence theorem is proved, and numerical examples are given.
R. N. Castleton, Some Numerical Methods for Differential Equations with Deviating Arguments, M.S. Thesis, University of Utah, 1970.
R. N. Castleton & L. J. Grimm, "Local existence and uniqueness for neutral functional equations." (In preparation.)
M. A. Feldstein, Discretization Methods for Retarded Ordinary Differential Equations, Ph.D. Thesis, University of California, Los Angeles, Calif., 1964.
- L. J. Grimm, Existence and continuous dependence for a class of nonlinear neutral-differential equations, Proc. Amer. Math. Soc. 29 (1971), 467–473. MR 287117, DOI 10.1090/S0002-9939-1971-0287117-1
- © Copyright 1973 American Mathematical Society
- Journal: Math. Comp. 27 (1973), 571-577
- MSC: Primary 65L05
- DOI: https://doi.org/10.1090/S0025-5718-1973-0343621-9
- MathSciNet review: 0343621