Page 427 - Excel for Scientists and Engineers: Numerical Methods

404 EXCEL: NUMERICAL METHODS

Runge3
Performs fourth-order Runge-Kutta integration of a system of N ordinary differential
equations. Returns the values of the N independent variables y at x + bit based on
specified values of x and the N independent variables y at x, and N differential
equations.

Syntax
Ru nge3 (x-variable, y- variables, deriv- formulas, interval, index)
x-varia ble the value of x
y- variables the array of y values at x
deriv-formulas the array of differential equations dyldx = F(x-variable, y-variable), in
the same order as y-variables
interval AX, the interval for the calculation
index an optional argument specifying which one of the array of y-variables
to be returned; if omitted, returns the complete array

Remarks
The argument x-variable can be a value, or a reference to a cell containing a value
or a formula.
The argument y-variables can be an array of values, or of references to cells
containing values or formulas.
The argument deriv-s is an array of references to cells containing values or
formulas. The array must be in the in the same order as y-variables.
The argument interval can be a value or a formula, or a reference to a cell
containing a value or a formula.
The optional argument index can be a value or a formula, or a reference to a cell
containing a value or a formula.
The workbook can be set to either R1C1- or Al-style.
The Runge3 function is an array function. If you omit the optional argument index,
you must select a horizontal range of cells, enter the function and then press
CONTROL+SHIFT+ENTER (Windows) or COMMAND+RETURN or
CONTROL+SHI~+RETURN (Macintosh).

Limitations
None of the precedent cells of the argument expression may contain references to
the argument reference.
The function cannot handle implicit references; that is, a name or range reference
cannot be used for a range of values.

See Also
Runge, Rungel