NUMAL Section 5.2.1.1.1.2

BEGIN SECTION : 5.2.1.1.1.2 (November, 1976)

SECTION 5.2.1.1.1.2 CONTAINS SIX ALTERNATIVE PROCEDURES FOR SOLVING
FIRST-ORDER INITIAL VALUE PROBLEMS WITH THE JACOBIAN MATRIX AVAILABLE.

Section 5.2.1.1.1.2.A:
A.  EFSIRK SOLVES AN INITIAL VALUE PROBLEM, GIVEN AS AN AUTONOMOUS
    SYSTEM OF FIRST ORDER DIFFERENTIAL EQUATIONS DY/DX = F(Y), BY
    MEANS OF AN EXPONENTIALLY FITTED, SEMI-IMPLICIT RUNGE-KUTTA
    METHOD; IN PARTICULAR THIS PROCEDURE IS SUITABLE FOR THE
    INTEGRATION OF STIFF EQUATIONS.

Section 5.2.1.1.1.2.B:
B.  EFERK SOLVES INITIAL VALUE PROBLEMS, GIVEN AS AN AUTONOMOUS SYSTEM
    OF FIRST ORDER DIFFERENTIAL EQUATIONS, BY MEANS OF AN EXPONENTIALLY
    FITTED, EXPLICIT RUNGE KUTTA METHOD OF THIRD ORDER, WHICH INVOLVES
    THE USE OF THE JACOBIAN MATRIX. AUTOMATIC STEP CONTROL IS PROVIDED.
    IN PARTICULAR  THIS METHOD IS SUITABLE FOR THE INTEGRATION OF STIFF
    DIFFERENTIAL EQUATIONS.

Section 5.2.1.1.1.2.C:
C.  LINIGER1VS SOLVES INITIAL VALUE PROBLEMS, GIVEN AS AN AUTONOMOUS
    SYSTEM OF FIRST ORDER DIFFERENTIAL EQUATIONS, BY MEANS OF AN
    IMPLICIT, FIRST ORDER ACCURATE, EXPONENTIALLY FITTED ONESTEP
    METHOD.
    AUTOMATIC STEPSIZE CONTROL IS PROVIDED.

Section 5.2.1.1.1.2.D:
D.  LINIGER2 SOLVES INITIAL VALUE PROBLEMS, GIVEN AS AN AUTONOMOUS
    SYSTEM OF FIRST ORDER DIFFERENTIAL EQUATIONS, BY MEANS OF AN
    EXPONENTIALLY FITTED ONESTEP METHOD.
    NO AUTOMATIC STEPSIZE CONTROL IS PROVIDED.

Section 5.2.1.1.1.2.E:
E.  GMS SOLVES AN INITIAL VALUE PROBLEM, GIVEN AS AN AUTONOMOUS SYSTEM
    OF FIRST ORDER DIFFERENTIAL EQUATIONS DY / DX = F(Y), BY MEANS OF A
    THIRD ORDER GENERALIZED LINEAR MULTISTEP METHOD.

Section 5.2.1.1.1.2.F:
F.  IMPEX SOLVES AN INITIAL VALUE PROBLEM,GIVEN AS AN AUTONOMOUS SYSTEM
    OF FIRST ORDER DIFFERENTIAL EQUATIONS, BY MEANS OF THE IMPLICIT
    MID-POINT RULE WITH SMOOTHING AND EXTRAPOLATION.
    AUTOMATIC STEPSIZE CONTROL IS PROVIDED.

IN PARTICULAR ALL THESE METHODS ARE SUITABLE FOR THE INTEGRATION OF
STIFF DIFFERENTIAL EQUATIONS.