项目作者: planelles20

项目描述 :
Solving linear, nonlinear equations, ordinary differential equations, ... using numerical methods in fortran
高级语言: Fortran
项目地址: git://github.com/planelles20/numerical-methods-fortran.git
创建时间: 2017-01-19T10:53:47Z
项目社区:https://github.com/planelles20/numerical-methods-fortran

开源协议:GNU General Public License v2.0

下载


Numerical methods in fortran

Solving linear, nonlinear equations, integral, ordinary differential equations, … using numerical methods in fortran

1. Linear equations:

  1. LU
  2. PLU (TODO)
  3. QR (TODO)

2. Non-uniform random number generator

  1. Normal distribution
  2. - BoxMuller transform
  3. - Ratio-of-uniforms method

3. Nonlinear equations

  1. Newton-Raphson
  2. Fix point

4. Integration Methods

  1. One-dimensional
  2. - Rectangle rule.
  3. - Trapezoidal rule.
  4. - Simpson's rule.
  5. - Gauss-Hermite (TODO)
  6. - Gauss-Laguerre (TODO)
  7. N-dimensional
  8. - Monte Carlo (TODO)
  9. - Sparse grids (TODO)
  10. - Bayesian Quadrature (TODO)

5. Ordinary differential equations (ODE)

  1. Monostep
  2. - Euler explicit
  3. - Euler implicit (TODO)
  4. - Runge-Kutta fourth order method (classical)
  5. Multistep
  6. - Adams-Bashforth
  7. - Adams-Moulton (TODO)
  8. - Nyström (TODO)
  9. - Mile-Simpson (TODO)
  10. - Backward differentiation formula (TODO)

6. Stochastic Ordinary Differential Equations (SDE)

  1. - Euler-Maruyama method
  2. - Milstein Method (TODO)
  3. - Strong Order 1.0 Runge-Kutta Method
  4. - Strong Order 1.5 Taylor Method (TODO)
  5. - Weak Order 2 Taylor Method (TODO)
  6. - Weak Order 2 Runge-Kutta Method

Examples

pgplot and dislin libraries are necessary to plot the examples:
pgplot, dislin

Example 1: ordinary differential equation


example ode equation


ordinary differential equation figure

Example 2: Lotka–Volterra 1


lotka_volterra 1 equation


lotka_volterra 1 figure

Example 3: Lotka–Volterra 2


lotka_volterra 2 equation


lotka_volterra 2 figure


transesterification equation

Where:


  • [TG] Triglycerides.

  • [DG] Diglycerides.

  • [MG] Monoglycerides.

  • [GL] Glycerin.

  • [A] Alcohol.

  • [E] Ethylester.


transesterification figure

Example 5: Bogdanov-Takens bifurcation


Bogdanov-Takens equation


Bogdanov-Takens figure

Example 6: pendulum


pendulum equation


pendulum figure

Example 7: Lorenz system


Lorenz equation


Lorenz figure

Example 8: Stochastic Ordinary Differential Equation (SDE)

Force Regulation by Nascent Adhesion Sites (Robijn Bruinsma)


one-dimensional integral equation


one-dimensional integral equation

Where:


  • G(0,1) standard normal distribution.


one-dimensional function figure