A new computational scheme in an attempt to improve the Taylor-Galerkin method is developed. Taylor-Galerkin method expresses the governing equations of motion in conservation form. The temporal discretization is done first and then spatial discretization follows, unlike the conventional approaches where the Galerkin finite element method is employed with standard time-discretization method.
In this study, an effective and efficient numerical scheme is developed by employing the third order term in the Taylor series of the fundamental variable. Taylor-Galerkin method used by others employs terms up to second order. The stability characteristics and accuracy of the proposed scheme are mathematically analyzed. The scheme is successfully applied to several numerical problems and is demonstrated for its superiority in many aspects against other existing time-integration schemes such as Newmark method as well as plain Taylor-Galerkin method.