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.