MtxIntDiff.WeightsNewtonCotes Function

Newton-Cotes base points and weights.

Pascal

procedure WeightsNewtonCotes(PolyOrder: Integer; const Points: TVec; const Weights: TVec; const FloatPrecision: TMtxFloatPrecision = mvDouble);

File

MtxIntDiff

Parameters

Parameters	Description
PolyOrder	Defines the interpolating polynomial order.
Points	Returns base points coordinate.
Weights	Returns weights.
FloatPrecision	Specifies the precision of the weights to be returned.

Description

Uses the Newton-Cotes formulas to calculate base points and weights for numerical integration. Check the following linkto learn more about Newton-Cotes formulas.

See Also

WeightsChebyshevGauss, WeightsGauss

Example

Use Simpson rule to evaluate sin(x) on interval [0,PI].

// Integrating function function IntFunc(const Parameters: TVec; const Constants: TVec; const ObjConst: Array of TObject): double; var x: double; begin x := Parameters[0]; IntFunc := Sin(x); end; // Integrate procedure DoIntegrate; var bpoints,weights: Vector; area: double; begin WeightsNewtonCotes(2,bpoints,weights); // 2 means Simpson area := QuadGauss(IntFunc,0,PI,bpoints,weights,1); end;

#include "MtxExpr.hpp" #include "Math387.hpp" #include "MtxIntDiff.hpp" // Integrating function double __fastcall IntFun(TVec* const Parameters, TVec* const Constants, System::TObject* const * ObjConst, const int ObjConst_Size) { double x = (*Parameters)[0]; return Math.Sin(x)*Math.Exp(-x*x); } void __fastcall Example(); { Vector bpoints, weights; WeightsNewtonCotes(2,bpoints,weights); double area = QuadGauss(IntFun,-0.5*PI,PI,bpoints,weights,1); }

MtxIntDiff, Functions, Example, See Also

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