Series solutions of linear ODEs by Newton-Raphson method on quotient
$D$-modules
Series solutions of linear ODEs by Newton-Raphson method on quotient
$D$-modules
We develop a $D-$module approach to various kinds of solutions to several classes of important differential equations by long divisions of different differential operators. The zeros of remainder maps of such long divisions are handled by an analogue of Hensel's lemma established recently from valuation theory. In particular, this explains …