A new approach to the discretization of chaplygin’s method

5. Conclusion

Chaplygin’s method is not convenient for the application in analytical form. However, the discretization of this method can be made successfully. The method of discretization described in this work is easy for the program-ming and, in some cases, gives better results than the Runge—Kutta method. Specifically, this happens when the steph is relatively small. It is highly un-likely that more than 6 iterations are necessary to achieve full accuracy, with 3 iterations being the most usual case.

The fact that the upper and lower Chaplygin’s boundary functions be-come almost identical after several iterations (in the sense of the floating point representation of their values on the grid) did not produce noticeable problems, even though it means evident departure from the assumptions of Chaplygin’s Theorem (specifically, the solution of the differential equation ceases to be bounded by the lower and upper functions). Nevertheless, the definite conclusion on this subject requires further theoretical investigation.