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### IMSL_INTFCN: Two-dimensional Iterated Integrals

IMSL_INTFCN: Two-dimensional Iterated Integrals

This version of the IMSL_INTFCN function integrates two-dimensional iterated integrals. To use this integration method, supply the TWO_DIMENSIONAL keyword.

This routine requires an IDL Advanced Math and Stats license. For more information, contact your sales or technical support representative.

This method approximates the following two-dimensional iterated integral:

The lower-numbered rules are used for less smooth integrands, while the higher-order rules are more efficient for smooth (oscillatory) integrands.

If this method is used, the function should be coded to protect endpoint singularities if they exist.

## Example

This example computes the value of the integral:

.RUN
; Define the function to be integrated.
FUNCTION f, x, y
RETURN, SIN(x + y)
END

.RUN
; Define the function for the lower limit of the inner integral.
FUNCTION g, x
RETURN, x
END

.RUN
; Define the function for the upper limit of the inner integral.
FUNCTION h, x
RETURN, 2 * x
END

ans = IMSL_INTFCN('f',0,1,'g','h',/Two_Dimensional)
; Call IMSL_INTFCN with keyword Two_Dimensional set and the names
; of the functions defining the limits of the inner integral.
PM, 'Computed Answer:', ans

IDL prints:

0.407609
exact = -SIN(3)/3 + SIN(2)/2

PM, 'Exact - Computed:', exact - ans

IDL prints:

Exact - Computed:
-5.96046e-08

## Syntax

Result = IMSL_INTFCN(F, A, B, G, H, /TWO_DIMENSIONAL)

## Return Value

The value of:

is returned. If no value can be computed, the floating-point value NaN (Not a Number) is returned.

## Arguments

### F

A scalar string specifying the name of a user-supplied function to be integrated. The function f accepts one scalar parameter and returns a single scalar of the same type.

### A

A scalar expression specifying the lower limit of integration.

### B

A scalar expression specifying the upper limit of integration.

### g

Scalar string specifying the name of a user-supplied IDL Advanced Math and Stats function used to evaluate the lower limit of the inner integral. Function g accepts one scalar parameter and returns a single scalar of the same type.

### H

Scalar string specifying the name of a user-supplied IDL Advanced Math and Stats function used to evaluate the upper limit of the inner integral. Function h accepts one scalar parameter and returns a single scalar of the same type.

## Keywords

In addition to the global IMSL_INTFCN keywords, the following keyword is available:

### TWO_DIMENSIONAL (optional)

Set this keyword to integrate a two-dimensional iterated integral.

## Version History

 6.4 Introduced