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Einzel-FIGL-Loeser.cpp File Reference

#include <iostream>
#include <fstream>
#include <vector>
#include <string>
#include "dim2taylor.hpp"
#include "itaylor.hpp"
#include "ilss.hpp"
#include "interval.hpp"
#include "ivector.hpp"
#include "intvector.hpp"
#include "imatrix.hpp"
#include "dot.hpp"
#include "idot.hpp"
#include "Einzel-FIGL-Loeser.hpp"

Functions

interval Imid (interval &I)
itaylor blow (itaylor &it, real eps)
ivector Powers (interval baseInt, int ord)
void Monom_Integration (ivector &Int_a, ivector &Int_b, int intord, interval T)
itaylor Iteration (IntegralOperatorRG &IntOp, itaylor &fkt_g, int ord, interval S, ivector &Int_a, ivector &Int_b, int &err)
ostream & operator<< (ostream &os, IntegralGleichung &IGL)

Detailed Description

VFIS Integral Equation Solver central module with all central methods/functions. Class definitions see header file.

Function Documentation

itaylor blow itaylor it,
real  eps
 

Epsilon inflation for itaylor arguments (elementwise).

Parameters:
[in] it itaylor object
[in] eps Epsilon
Returns:
The inflated itaylor object

interval Imid interval &  I  ) 
 

Interval Midpoint Computation with interval result.

Parameters:
[in] I The interval
Returns:
The midpoint

itaylor Iteration IntegralOperatorRG IntOp,
itaylor fkt_g,
int  ord,
interval  S,
ivector &  Int_a,
ivector &  Int_b,
int &  err
 

Part I: Iteration function: Carries out the fixed point iteration

y_0=g; y_{i+1}=IntOp(y_i)

for an integral operator IntOp

Parameters:
[in] IntOp The integral operator of the iteration
[in] fkt_g g as in formula above
[in] ord Taylor order in use
[in] S Domain of the function
[in] Int_a Integrals of powers of basic monomials
[in] Int_b Integrals of powers of basic monomials
[out] err Error code
Returns:
itaylor representation of the result

void Monom_Integration ivector &  Int_a,
ivector &  Int_b,
int  intord,
interval  T
 

Computes integrals of basic monomials.

Parameters:
[out] Int_a Given a domain T:=[a,b] with midpoint t0, the integrals of (a-t0)^k, k=0..intord, are computed and stored in Int_a
[out] Int_b Given a domain T:=[a,b] with midpoint t0, the integrals of (b-t0)^k, k=0..intord, are computed and stored in Int_b
[in] intord Maximum order of integral computation
[in] T domain

ostream& operator<< ostream &  os,
IntegralGleichung IGL
 

Output operator for class IntegralGleichung objects

Parameters:
[in,out] os Output stream
[in] IGL IntegralGleichung object reference
Returns:
Output stream

ivector Powers interval  baseInt,
int  ord
 

Computes powers I^j, j=1..n, for a given interval.

Parameters:
[in] baseInt interval
[in] ord maximum exponent
Returns:
ivector containing I^j, j=1..n


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