NUMAL Section 5.2.1.1.1.3

BEGIN SECTION : 5.2.1.1.1.3 (August, 1974)

SECTION 5.2.1.1.1.3 CONTAINS TWO  ALTERNATIVE PROCEDURES FOR SOLVING
FIRST-ORDER INITIAL VALUE PROBLEMS WITH SEVERAL DERIVATIVES AVAILABLE.

Section 5.2.1.1.1.3.A:
A.  MODIFIED TAYLOR SOLVES AN INITIAL ( BOUNDARY ) VALUE PROBLEM, GIVEN
    AS A SYSTEM OF  FIRST ORDER DIFFERENTIAL EQUATIONS , BY MEANS OF A
    ONE-STEP TAYLOR-METHOD.
    IN PARTICULAR THIS METHOD IS SUITABLE FOR THE INTEGRATION OF LARGE
    SYSTEMS ARISING FROM PARTIAL DIFFERENTIAL EQUATIONS, PROVIDED THAT
    HIGHER ORDER DERIVATIVES CAN BE EASILY OBTAINED.

Section 5.2.1.1.1.3.B:
B.  EXPONENTIALLY FITTED TAYLOR  SOLVES AN INITIAL VALUE PROBLEM, GIVEN
    AS A SYSTEM  OF  FIRST ORDER DIFFERENTIAL EQUATIONS , BY MEANS OF A
    ONE-STEP  TAYLOR-METHOD . AUTOMATIC  STEPSIZE  CONTROL IS PROVIDED.
    IN PARTICULAR THIS METHOD IS SUITABLE FOR THE INTEGRATION OF  STIFF
    DIFFERENTIAL EQUATIONS , PROVIDED THAT HIGHER ORDER DERIVATIVES CAN
    BE EASILY OBTAINED.