BVPNonIdentityMatrix0.cpp File Reference

Solving the equation. More...

#include <BVP_bundle.h>

Go to the source code of this file.

Classes
class	CppNoddy::Example::Nonidentity_equation< _Type, _Xtype >
	Define the harmonic equation by inheriting the Equation base class. More...
class	CppNoddy::Example::Nonidentity_left_BC< _Type >
class	CppNoddy::Example::Nonidentity_right_BC< _Type >

Namespaces
namespace	CppNoddy
	A collection of OO numerical routines aimed at simple (typical) applied problems in continuum mechanics.
namespace	CppNoddy::Example

Enumerations
enum	{ f , fd }

Functions
int	main ()

Detailed Description

Solving the equation.

subject to and . We don't divide by the that multiplies the highest derivative, rather we define a non-identity matrix0. The solution is compared at all nodes to the exact solution

Definition in file BVPNonIdentityMatrix0.cpp.

Enumeration Type Documentation

anonymous enum

anonymous enum

Enumerator
f
fd

Definition at line 15 of file BVPNonIdentityMatrix0.cpp.

{f, fd };

Function Documentation

main()

int main

(

)

Definition at line 80 of file BVPNonIdentityMatrix0.cpp.

{
  cout << "\n";
  cout << "=== BVP: finite-difference, non-identity matrix0 ====\n";
  cout << "\n";
 
  Example::Nonidentity_equation<double, double> problem;
  Example::Nonidentity_left_BC <double> BC_left;
  Example::Nonidentity_right_BC<double> BC_right;
 
  double left =  0.0;
  double right = 1.0;
  // number of nodal points
  unsigned N = 151;
  // a real mesh -- along real axis
  DenseVector<double> nodes( Utility::uniform_node_vector( left, right, N ) );
  // Example tolerance
  const double tol = 1.e-4;
 
  // a real ODE BVP
  problem.gamma = 5.0;
  ODE_BVP<double> ode( &problem, nodes, &BC_left, &BC_right );
 
  // our initial guess
  for ( unsigned i = 0; i < N; ++i )
  {
    double y = ode.solution().coord( i );
    // set f(y)
    ode.solution()( i, f ) = 1+y;
    // set f'(y)
    ode.solution()( i, fd ) = 1;
  }
 
  // solve the problem using 2nd order finite-difference
  try
  {
    ode.solve2();
  }
  catch (const std::runtime_error& error )
  {
    cout << " \033[1;31;48m  * FAILED THROUGH EXCEPTION BEING RAISED \033[0m\n";
    return 1;
  }
 
 
  // find deviation from exact solution
  double diff = 0;
  for ( unsigned i = 0; i < N; ++i )
  {
    const double y( ode.solution().coord(i) );
    const double exact( sqrt(y*y + problem.gamma*y*y*y/3 + (2-problem.gamma/3)*y + 1) );
    diff = std::max( std::abs( ode.solution().get_interpolated_vars(y)[f] - exact ), diff );
  }
 
  // validation test
  if ( diff > tol )
  {
    cout << "\033[1;31;48m  * FAILED \033[0m\n";
    cout << "Real problem error " << diff << "\n";
    return 1;
  }
  else
  {
    cout << "\033[1;32;48m  * PASSED \033[0m\n";
    return 0;
  }
}

References f, fd, CppNoddy::Example::Nonidentity_equation< _Type, _Xtype >::gamma, CppNoddy::ODE_BVP< _Type, _Xtype >::solution(), CppNoddy::ODE_BVP< _Type, _Xtype >::solve2(), and CppNoddy::Utility::uniform_node_vector().