| Abstract: | The Galerkin and subdomain forms of the weighted residual method are used to generate recursive equations in time for the numerical solution of a system of ordinary differential equations. The single-step methods that result from a linear interpolation equation match currently available methods whose stability and oscillation properties are known. A three-level scheme developed by combining two linear elements is shown to be unconditionally unstable. Two of the three schemes obtained using a quadratic interpolation equation and quadratic weighting functions are also shown to be unconditionally unstable. The third scheme is unconditionally stable, but the calculated values for a numerical solution of u? + u = 0, u(0) = 1 are not as accurate as the values obtained using the single-step central difference method. |
