HP 48GII User Manual

3-154 Full Command and Function Reference
–
The partial derivative of y'(t) with respect to the independent variable (or a variable where
the expression is stored).
• x
tol
sets the tolerance value. If a list is used, the first value is the tolerance and the second
value is the initial candidate step size.
• x
Tfinal
specifies the final value of the independent variable.
RRK repeatedly calls RKFSTEP as its steps from the initial value to x
Tfinal
.
Access: …µ
RRK
Input/Output:
L
3
/A
1
L
2
/A
2
L
1
/A
3
L
2
/I
1
L
1
/I
2
{ list } x
tol
x
T final
→
{ list } x
tol
{ list } { x
tol
x
hstep
} x
T final
{ list } x
tol
L = Level; A = Argument; I = item
See also: RKF, RKFERR, RKFSTEP, RRKSTEP, RSBERR
RRKSTEP
Type: Command
Description: Next Solution Step and Method (RKF or RRK) Command: Computes the next solution step
(h
next
) to an initial value problem for a differential equation, and displays the method used to
arrive at that result.
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).
• x
tol
is the tolerance value.
• h specifies the initial candidate step.
• last specifies the last method used (RKF = 1, RRK = 2). If this is the first time you are using
RRKSTEP, enter 0.
• current displays the current method used to arrive at the next step.
• h
next
is the next candidate step.
The independent and solution variables must have values stored in them. RRKSTEP steps these
variables to the next point upon completion.
Note that the actual step used by RRKSTEP will be less than the input value h if the global error
tolerance is not satisfied by that value. If a stringent global error tolerance forces RRKSTEP to
reduce its stepsize to the point that the Runge–Kutta–Fehlberg or Rosenbrock methods fails,
then 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
-499
or if the variable is nonzero and the stepsize is 2.5 × 10
-11
times its magnitude. The Runge–Kutta–Fehlberg method will fail if the current independent
variable is zero and the stepsize ≤ 1.3 × 10
-498
or if the variable is nonzero and the stepsize is 1.3
× 10
-10
times its magnitude.
Access: …µ
RRKS

HP 48GII Specifications

General

Battery type	CR2032
Type	Scientific
Form factor	Pocket

Weight and Dimensions

Weight	220 g
Dimensions (WxDxH)	184 x 87 x 23.5 mm

Summary

RPL Programming

Understanding Programs

Programs as objects, delimiters, and basic structure.

Entering and Executing Programs

Details on how to create, store, and run programs.

Using Conditional Structures

Covers IF, CASE, IFT, IFTE structures for program decision-making.

Input and Output Commands

Details commands like PROMPT, INPUT, INFORM, CHOOSE for user interaction.

RPL Programming Examples

Fibonacci Numbers

Demonstrates recursive and loop-based Fibonacci calculations.

Minimum and Maximum Array Elements

Details finding min/max elements using MNX and MNX2.

Applying a Program to an Array

Explains the APLY command for transforming array elements.

Full Command and Function Reference

How to Access Commands and Functions

Explains key presses and menu paths to access commands.

ABS (Absolute Value)

Details the absolute value function and its array behavior.

ACOS (Arc Cosine)

Explains the inverse cosine function, domain, and range.

Computer Algebra Commands

CAS Operations

Overview of CAS operations and their categorization by menu.

Algebra commands

Lists and describes commands for algebraic manipulation.

Calculus Commands

Covers derivation, integration, and limit commands.

Equation Reference

Columns and Beams (1)

Provides equations for structural mechanics.

Electricity (2)

Lists equations related to electrical circuits and laws.

Fluids (3)

Covers equations for fluid mechanics.

The Development Library

Introduction

Explains the purpose and usage of the development library.

Tools for Development

Details APEEK, PEEK, POKE, POKEARM commands.

MASD Compiler

Discusses syntax, modes, and directives for MASD.

Error and Status Messages

Messages Listed Alphabetically

Alphabetical list of error messages.

Messages Listed Numerically

Numerical list of error messages by hex code.

System Flags

System Flags (continued)

Description of various system flags.

System Flags (continued)

Continuation of system flags description.

Reserved Variables

Contents of the Reserved Variables

Explanation of key reserved variables.

PPAR

Details plotting parameters.

Technical Reference

Object Sizes

Lists object sizes in bytes.

Symbolic Integration Patterns

Provides a table of symbolic integration patterns.

Parallel Processing With Lists

General rules for parallel processing

Explains conditions for parallel list processing.

Group 4: ADD and +

Describes how ADD and + handle parallel list operations.

Keyboard Shortcuts

Press and Hold key combinations

Lists functions performed by key combinations.

Shifted softkeys

Explains shift key effects on menu labels.

The Menu-Number Table

-- menus 0-117 are semi-compatible with 48G menus --

Menu numbers and paths for built-in menus.

-- New Library 222 commands --

Details commands available in Library 222.