README.md

java.math.numerical.library

Java numerical library is based on numerical methods (https://en.wikipedia.org/wiki/Numerical_method) and it was tested using Matlab/Octave (https://www.gnu.org/software/octave/)

Java numerical library features:

• Functions (https://en.wikipedia.org/wiki/Function_(mathematics))

• Functions with n vars (https://en.wikipedia.org/wiki/Function_of_several_real_variables)

  • Math expression parser: java.math.expression.parser that you can find in my github repository. It is a recursive ascent parser

• Equations solver (https://en.wikipedia.org/wiki/Equation)

  • Numerical methods to solve equations
    • Dichotomy (https://en.wikipedia.org/wiki/Bisection_method)
    • Newton–Raphson (https://en.wikipedia.org/wiki/Newton%27s_method)

• System of equation solver (https://en.wikipedia.org/wiki/System_of_linear_equations)

• Sytems of nonlinear equation solver (https://en.wikipedia.org/wiki/Nonlinear_system)

    String equation1 = "2.35*e^(-3)*(x+y)^1.75-75+z";
    String equation2 = "4.67*e^(-3)*x^1.75+20-z";
    String equation3 = "3.72*e^(-2)*y^1.75+15-z";
  

• System of ODE solver (https://en.wikipedia.org/wiki/Ordinary_differential_equation)

  • Numerical methods to solve System of ODE
    • Runge-Kutta (https://en.wikipedia.org/wiki/Runge%E2%80%93Kutta_methods)
    • Predictor-Corrector (https://en.wikipedia.org/wiki/Predictor%E2%80%93corrector_method)

• Cauchy equation (https://en.wikipedia.org/wiki/Cauchy_problem)

  • (https://www.encyclopediaofmath.org/index.php/Cauchy_problem,_numerical_methods_for_ordinary_differential_equations)
  • ODE equation: y'(x)= f(x,y); y(x0) = y0
  • numerical methods to solve the Cauchy Equation ( solution y(x) )
    • Runge-Kutta
    • Adaptative Runge-Kutta
    • Predictor - Corrector

• Dirichlet equation (https://en.wikipedia.org/wiki/Dirichlet_problem)

  • ODE equation: a(x)*y'' + b(x)*y' + c(x)*y = f(x)
  • Dirichlet boundary condition: y(a)=A , y(b)=B || A = alpha, B = Beta (https://en.wikipedia.org/wiki/Dirichlet_boundary_condition)

• Neumann equation

  • ODE equation: a(x)*y'' + b(x)*y' + c(x)*y = f(x)
  • Solutions for Neumann boundary conditions: (https://en.wikipedia.org/wiki/Neumann_boundary_condition)
    • y'(a)=A y'(b)=B || A = alpha, B = beta
    • y'(a)=A y(b)=B || A = alpha, B = beta
    • y(a)=A y'(b)=B || A = alpha, B = beta

• Vectors:

  • Basic math operations with vectors
  • Eclidean norm & Maximun norm https://en.wikipedia.org/wiki/Norm_(mathematics)

• Matrix

  • Basic math operations with matrix
  • Linear Algebra (https://en.wikipedia.org/wiki/Linear_algebra)
  • Inverse solver (https://en.wikipedia.org/wiki/Invertible_matrix)
  • Determinant solver (https://en.wikipedia.org/wiki/Determinant)
  • Identity matrix (https://en.wikipedia.org/wiki/Identity_matrix)
  • Balanced Matrix (https://en.wikipedia.org/wiki/Balanced_matrix)
  • Householder matrix (https://en.wikipedia.org/wiki/Householder_transformation)
  • Hessenber matrix (https://en.wikipedia.org/wiki/Hessenberg_matrix)
  • Eigenvalues & eigenvectors calculator (https://en.wikipedia.org/wiki/Eigenvalues_and_eigenvectors)
    • numerical methods to calculate Eigenvalues:
      • Power Iteration (https://en.wikipedia.org/wiki/Power_iteration)
      • QR Algorithm (https://en.wikipedia.org/wiki/QR_algorithm)
    • numerical method to calculate eigenvectors
      • Inverse iteration https://en.wikipedia.org/wiki/Inverse_iteration

• Integrals: This library can solve integrals using numerical integration (https://en.wikipedia.org/wiki/Numerical_integration):

  • Integrals: numerical methods to solve integrals (https://en.wikipedia.org/wiki/Integral)
    • Trapezoidal (https://en.wikipedia.org/wiki/Trapezoidal_rule)
    • Simpson (https://en.wikipedia.org/wiki/Simpson%27s_rule)
    • Romberg (https://en.wikipedia.org/wiki/Romberg%27s_method
  • Multidimensional Integrals: (https://en.wikipedia.org/wiki/Multiple_integral)
    • QuasiMontecarlo: (https://en.wikipedia.org/wiki/Quasi-Monte_Carlo_method) numerical method to solve multidimensional integrals

• Derivatives: This library can solve derivatives using numerical diferenciation (https://en.wikipedia.org/wiki/Numerical_differentiation)

  • Derivatives (https://en.wikipedia.org/wiki/Derivative)

  • Partial derivatives (https://en.wikipedia.org/wiki/Partial_derivative)

• Polynomials with real & complex coefficients (https://en.wikipedia.org/wiki/Polynomial)

  • Root or zero of a polynomial solver (https://en.wikipedia.org/wiki/Zero_of_a_function)
    • Laguerre: (https://en.wikipedia.org/wiki/Laguerre%27s_method) numerical method to calculate roots

• Series solver (https://en.wikipedia.org/wiki/Series_(mathematics))

  • function series: functions with one or n real vars (https://en.wikipedia.org/wiki/Function_series)

• Complex Numbers (https://en.wikipedia.org/wiki/Complex_number)

• Combination (https://en.wikipedia.org/wiki/Combination)

• Factorial (https://en.wikipedia.org/wiki/Factorial)

There are examples in the test folder

Reference Book: Numerical recepies in C (https://en.wikipedia.org/wiki/Numerical_Recipes)

Professional Services

If you are interested in logical parsers or any task related to parsers, you can consult my professional services page https://github.com/sbesada/professional.services

Donation

If you think that my work deserves a donation, you can do it: https://sbesada.github.io/