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§5.7(i) Maclaurin and Taylor Series… ►For 15D numerical values of see Abramowitz and Stegun (1964, p. 256), and for 31D values see Wrench (1968). ►
§3.7(ii) Taylor-Series Method: Initial-Value Problems… ►
§3.7(iii) Taylor-Series Method: Boundary-Value Problems… ►It will be observed that the present formulation of the Taylor-series method permits considerable parallelism in the computation, both for initial-value and boundary-value problems. … ►General methods for boundary-value problems for ordinary differential equations are given in Ascher et al. (1995). … ►The method consists of a set of rules each of which is equivalent to a truncated Taylor-series expansion, but the rules avoid the need for analytic differentiations of the differential equation. …
Corless et al. (1992) describe a method of approximation based on subdividing into a triangular mesh, with values of , stored at the nodes. and are then computed from Taylor-series expansions centered at one of the nearest nodes. The Taylor coefficients are generated by recursion, starting from the stored values of , at the node. Similarly for , .