RRKSTEP will use the Euler method to compute the next solution step and will consider the error tolerance satisfied. The Rosenbrock method will fail if the current independent variable is zero and the stepsize ≤ 2.5 × 10-499or if the variable is nonzero and the stepsize is 2.5 × 10-11times its magnitude. The Runge–Kutta–Fehlberg method will fail if the current independent variable is zero and the stepsize ≤ 1.3 × 10-498or if the variable is nonzero and the stepsize is 1.3 × 10-10times its magnitude.

Access:

…µRRKS

 

 

 

 

 

 

 

Input/Output:

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

L4/A1

L3/A2

L2/A3

L1/A4

L4/I1

L3/I2

L2/I3

L1/I4

 

 

 

 

 

 

 

 

 

 

 

 

{ list }

xtol

h

last →

{ list }

xtol

hnext

current

 

 

 

 

 

 

 

 

 

 

 

L = Level; A = Argument; I = item

 

 

 

 

See also:

RKF, RKFERR, RKFSTEP, RRK, RSBERR

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

RSBERR

Command

 

 

 

 

 

 

 

Type:

 

 

 

 

 

 

 

Description:

Error Estimate for Rosenbrock Method Command: Returns an error estimate for a given step h

 

when solving an initial values problem for a differential equation.

 

 

 

The arguments and results are as follows:

•{ list } contains five items in this order:

–The independent variable (t).

–The solution variable (y).

–The right-hand side of the differential equation (or a variable where the expression is stored).

–The partial derivative of y'(t) with respect to the solution variable (or a variable where the expression is stored).

–The partial derivative of y'(t) with respect to the independent variable (or a variable where the expression is stored).

•h is a real number that specifies the initial step.

•ydelta displays the change in solution.

•error displays the absolute error for that step. The absolute error is the absolute value of the estimated error for a scalar problem, and the row (infinity) norm of the estimated error vector for a vector problem. (The latter is a bound on the maximum error of any component of the solution.) A zero error indicates that the Rosenbrock method failed and Euler’s method was used instead.

Access:

…µRSBER

 

 

 

 

 

 

Input/Output:

 

 

 

 

 

 

 

 

 

 

L2/A1

L1/A2

 

L4/I1

L3/I2

L2/I3

L1/I4

 

 

 

 

 

 

 

 

 

 

 

{ list }

h

→

{ list }

h

ydelta

error

 

 

 

 

 

 

 

 

 

 

L = Level; A = Argument; I = item

 

 

 

See also:

RKF, RKFERR, RKFSTEP, RRK, RRKSTEP

 

 

 

 

 

 

 

 

 

 

 

 

 

RSD

Command

 

 

 

 

 

 

Type:

 

 

 

 

 

 

Description:

Residual Command: Computes the residual B – AZ of the arrays B, A, and Z.

 

A, B, and Z are restricted as follows:

•A must be a matrix.

•The number of columns of A must equal the number of elements of Z if Z is a vector, or the number of rows of Z if Z is a matrix.

•The number of rows of A must equal the number of elements of B if B is a vector, or the number of rows of B if B is a matrix.

Full Command and Function Reference 3-213