AVDYUSHEV Victor (Scharm N)

About Me Papers Chair Software Scharm N What is God E-mail

Integrator Lobbie (New!)

Lobbie_I.for Lobbie_II.for Lobbie_III.for (pdf, 0.5Mb)

Kepler_Solver

The flash-project Kepler_Solver was designed for showing efficiency of numerical integration methods as applied to the plane two-body problem. In the project two groups of low-order methods were realized: Runge–Kutta (Euler, Heun and classical) and symplectic (Euler and two-order Stormer–Verlet). In every method exists a possibility for correcting a numerical solution for its deviation from the energy hypersurface (Nacozy's method). It allows one to preserve the energy integral and to improve the behavior of integration errors. All the methods run in two mode: either constant or variable step. The variable step is controlled proportionally to the radius-vector. The problem condition is assigned by the eccentricity specified by a user.

The display part of the flash-project represents a control board and a field of visualization of integration results. On the control board: RK1 is one of two Euler methods (of first-order); RK2 is Heun's and the trapezium method (of second-order); RK4 is the classical Runge–Kutta and a Gauss method (of forth-order); Iterations enables one to select either an explicit (Exp.) or an implicit (2–8) method (the number of iterations for solving a nonlinear system of equations inside the implicit method); SE1 is the Euler symplectic method (of first-order); LF2 is the leap–frog method or Stormer–Verlet method (of second-order); Projection is Nacozy's correction; Step enables one to select the step-size from 0.01 to 1; Variable is the variable step mode; Eccentricity is the orbital eccentricity from –0.9 to 0.9; Kepler switches on a visualization of the accurate orbit; Start/Stop starts or stops the numerical integration; Clear initializes the problem. All the control buttons (except Eccentricity and Kepler) also remain accessible during numerical integration. On the field of visualization the numerical (accurate) body's position and orbit are presented with a white (blue) point and a white (blue) curve respectively; on the top is shown the integration method used; at the foot is given the error in numerical position vector and the number of space body's revolutions (on the accurate orbit).

Gauss–Everhart Integrator

Gauss_15.for Gauss_32.for Gauss_32_mod.for (pdf, 0.2Mb, in Russian)

Adams–Moulton–Bashforth Integrator

AMB.for (pps, 1.2Mb, in Russian)

Gragg–Bulirsch–Stoer Integrator

GBS.for

Since Gauss_32_mod, AMB and GBS are beta I would be very much obliged for your comments, remarks and suggestions. Mail me.