Systems of Differential Equations [chapter]

Christian Constanda
2017 Springer Undergraduate Texts in Mathematics and Technology  
We propose algorithms for the computation of the first N terms of a vector (or a full basis) of power series solutions of a linear system of differential equations at an ordinary point, using a number of arithmetic operations that is quasi-linear with respect to N . Similar results are also given in the nonlinear case. This extends previous results obtained by Brent and Kung for scalar differential equations of order 1 and 2.
doi:10.1007/978-3-319-50224-3_7 fatcat:a5v3tq6sfjg5dmh2uyqd3ozdsi