3-point block methods for direct integration of general second-order ordinary differential equations (Q666386)

Summary: A multistep collocation technique is used to develop a 3-point explicit and implicit block method, which is suitable for generating solutions of the general second-order ordinary differential equations of the form \(y'' = f(x, y, y')\), \(y(x_0) = a\), \(y'(x_0) = b\). The derivation of both explicit and implicit block schemes is given for the purpose of comparison of results. The stability and convergence of the individual methods of the block schemes are investigated, and the methods are found to be 0-stable with good region of absolute stability. The 3-point block schemes derived are tested on standard mechanical problems, and it is shown that the implicit block methods are superior to the explicit ones in terms of accuracy.