A new approach to the discretization of Chaplygin's method (Q1297752)

An alternative is suggested to improve the so-called Chaplygin method for solving the Cauchy problem \(dy/dx=f(x,y)\), \(y(a)=y_0\). The accuracy of the method is increased by augmenting the trapezoidal rule with several members of the Euler-MacLaurin formula. It is shown that when all the derivatives so involved are approximated by finite differences of order \(2m+1\), then the accuracy of the Chaplygin method turns to be of order \(O(h^{2m+2})\).