MathAction NumericalIntegration

Topics

FrontPage
- OldWishList
  - NumericalIntegration <-- You are here.

The package NumericalQuadrature implements several operations for numerical integration. Here I provide just some examples. Documentation is to be found in the corresponding .spad or .pamphlet file.

fricas

(1) -> romberg(x+->exp(x),0.0,1.0,0.1,0.1,6,10)

$\label{eq1}\begin{array}{@{}l} \displaystyle \left[{value ={1.7182818284 \_ 590452354}}, \:{error ={0.0}}, \: \right. \ \ \displaystyle \left.{totalpts ={129}}, \:{success = \mbox{\rm true} }\right]$

(1)

Type: Record(value: Float,error: Float,totalpts: Integer,success: Boolean)

fricas

simpson(x+->exp(x),0.0,1.0,0.1,0.1,6,10)

$\label{eq2}\begin{array}{@{}l} \displaystyle \left[{value ={1.7182818284 \_ 590539174}}, \: \right. \ \ \displaystyle \left.{error ={2.1478522855 \_ 738173967}}, \:{totalpts ={102 5}}, \: \right. \ \ \displaystyle \left.{success = \mbox{\rm false} }\right]$

(2)

Type: Record(value: Float,error: Float,totalpts: Integer,success: Boolean)

fricas

trapezoidal(x+->exp(x),0.0,1.0,0.1,0.1,6,10)

$\label{eq3}\begin{array}{@{}l} \displaystyle \left[{value ={1.7182905680 \_ 834782946}}, \: \right. \ \ \displaystyle \left.{error ={0.0000327734 \<u> 5826871994 \</u> 1097}}, \:{totalpts ={129}}, \: \right. \ \ \displaystyle \left.{success = \mbox{\rm true} }\right]$

(3)

Type: Record(value: Float,error: Float,totalpts: Integer,success: Boolean)

Note that for some reason

fricas

%pi::Float

$\label{eq4}3.1415926535 \<u> 897932385$

(4)

Type: Float

works, while

fricas

%e::Float

   Cannot convert the value from type Expression(Integer) to Float .

fails. You have to use

fricas

exp(1)$Float

$\label{eq5}2.7182818284 \<u> 590452354$

(5)

Type: Float

instead.

Subject: Be Bold !!

	( 15 subscribers )