Here are the codes I made in the Numerical Methods 2 course in my Computer Science graduation at Federal University of Ceará, taught by Prof. Emanuele Santos. They were made in 2014 and maybe not fully functional.

• If you see any writing errors or typos, please warn me;
• Any doubts, sugestions and/or issues, please contact me.

• Compiling
  • Compiling Everything
  • Individual Compilation
• Executing
  • General Execution
  • Specific Execution
• General main files
  • Numerical Integration
  • Numerical Derivative
  • Initial Value Problems
  • Boundary Value Problems
  • Eigenvalues and Eigenvectors

• To compile all methods at the same time it is enough to go into the folder where Makefile is and use the make command:

$ make

• To compile only one method, use the corresponding make command.
• For this, you should go into the folder where the Makefile is and execute the help command:

$ make help

• To execute a method that has variations, you should execute the general main file of this method, whose last line argument should be the id of a specific method;
• E.g.: there are three specfic main files for Closed Newton-Cotes Methods: trapezoidal rule (1st order), Simpson's 1/3 rule (2nd order) and Simpson's 1/8 rule (3rd order).
• However, it is possible to execute a Closed Newton-Cotes method up to 6th order. For this, you should use the general main file, main_closedNewtonCotes.cpp, with the executable execClosedNC (you can verify it in $ make help). The execution should be:

$ ./execClosedNC inputfile.txt order

• Example:

$ ./execClosedNC entrada1.txt 6

• A general main file can be used to execute specific examples without problems. Specific main files are nothing more than a provided use of a general main file.
• For specific informations of every method, please see the Appendix.

• To execute a specific method, you should execute its own method with convenient arguments (you can verify it in $ make help).
• E.g.: to execute the trapezoidal rule without using the general main file your executable will be execTrapezium (please forgive my typo here, at that time I didn't know that the correct name is trapezoidal rule):

$ ./execTrapezium inputfile.txt

• main_closedNewtonCotes.cpp
  • Used to solve single integrals using Closed Newton-Cotes methods;
  • It accepts order from 1 to 6, where 1 is the trapezoidal rule, 2 is the Simpson's 1/3 rule and 3 is the Simpson's 3/8 rule.
• main_quadrature.cpp
  • Used to solve integrals using Gaussian Quadrature methods.
• main_doubleIntegration.cpp
  • Used to solve double integrals using Closed Newton-Cotes methods;
  • It accepts order from 1 to 6, where 1 is the trapezoidal rule, 2 is the Simpson's 1/3 rule and 3 is the Simpson's 3/8 rule.
• main_romberg.cpp
  • Used to solve double integrals using Romberg's method, which in turn uses Closed Newton-Cotes methods;
  • It accepts order from 1 to 6, where 1 is the trapezoidal rule, 2 is the Simpson's 1/3 rule and 3 is the Simpson's 3/8 rule.

• main_firstDerivative.cpp
  • Used to solve first derivatives using finite difference methods or Lagrange multiplier;
  • It accepts values from 0 to 2, where 0 is Backward Difference, 1 is Forward Difference and 2 is Central Difference;
  • To use the Lagrange multiplier method, you should use the specific main file main_lagrangeDerivative.cpp.
• main_richardsonExtrapolation.cpp
  • Used to solve first derivatives using Richardson extrapolation method, which in turn uses finite difference;
  • It accepts values from 0 to 2, where 0 is Backward Difference, 1 is Forward Difference and 2 is Central Difference.
• main_secondDerivative.cpp
  • Used to solve second derivatives using finite difference methods;
  • It accepts values from 0 to 2, where 0 is Backward Difference, 1 is Forward Difference and 2 is Central Difference.

• mainAdamsPredictorCorrector.cpp
  • It accepts order values of 0 or 1, where 0 is Adams Predictor-Corrector 3rd order and 1 is Adams Predictor-Corrector 4th order.
• mainRungeKutta.cpp
  • It accepts order values from 0 to 3, where 0 is Forward Euler method (Runge-Kutta 1st order), 1 is Runge-Kutta 2nd order, 2 is Runge-Kutta 3rd order and 3 is Runge-Kutta 4th order.

Please, see also the "Intructions" file inside the folder "BoundaryValueProblems"

• main_tridiagonalMatrx.cpp
  • Used to solve a linear system, represented by a tridiagonal matrix.
• main_gaussianElimination.cpp
  • Used to solve a linear system, represented by a two-dimensional matrix, using Gaussian ELimination.
• main_gaussSeidel.cpp
  • Used to solve a linear system, represented by a two-dimensional matrix, using Gauss-Seidel method.

Incomplete*

• main_powerIteration.cpp
• main_inverseIteration.cpp
• main_powerIteration.cpp
• main_jacobi.cpp
• main_qrAlgorithm.cpp
• main_householderTransformation.cpp