Numerical Methods for Solving Ordinary Equations – ODEs in C++

An ordinary differential equation – ODE, is solved using the following numerical method algorithms, coded in C++ language:

Euler

• Modified Euler
• Predictor-Corrector
• Runge Kutta (Order2)
• Runge Kutta (Order4)

HISTORY

Version 2 – 04-IV-2024

• Code is updated and improved
• Merges all numerical methods that solve differential equations in a single file
• Porting to VC++ 2017
• Translate functions name
• Change float variables to double
• The function y’ = f(x,y) is unified into a single function that is reused in all methods
• Unused variables are eliminated
• The ModifiedEuler and Predictor_Corrector method is corrected
• Order 4 Runge Kutta method added
• A menu is added in text mode to select the numerical method to use in the solution
• Unnecessary files are removed
• The code is modernized, converting it into the CNumericalMethodsSolvingODE class
• Traces of old C function fabs, etc… are removed and replaced with their modern equivalents
• The maximum width at which a menu box can be created is increased
• Change project name to SolvingODE
• Comments are translated from Spanish to English
• Credits are added
• The visualization of the x and y calculation tables is improved, in each method, always showing the values in the range [a, b]
• A chronometer is added to measure the time that each method takes, and the seconds that each method has taken to process the solution are shown, in order to obtain a point of comparison between the efficiency of the algorithms.
• The ShowSolutions method is added to display the solutions after the numerical method algorithm code has finished. In such a way that the time of each algorithm can be measured correctly and
  then display the results on the screen.
• The FormulaParser library is added to define an ODE y’=f(x,y) from a text string entered by the user, and in this way the user will be able to customize the ODE equation that will be solved by the numerical methods implemented.
• Added ExampleOfUse to the “Enter ODE: y’ = f(x,y)” option, to inform the user how to enter the formulation of the mathematical function

Version 1 – 30-XI-1999

• First version for Borland C++ 3.1 and Turbo C 3.0