Modified differential transformation method for solving nonlinear dynamic problems

•A family of explicit higher order time integration algorithms is presented.•First four members of this family are considered thoroughly.•The proposed techniques are based on the modified version of the differential transformation methods.•The numerical effects of both modified and current DTM procedures are compared.•Some numerical examples are performed to verify the proposed time integration method.

SummaryA family of explicit higher order time integration algorithms is presented. The proposed techniques are based on the modified version of the differential transformation methods. First four members of this family are considered thoroughly. To improve the numerical properties of the DTM scheme, two parameters are introduced in the displacement and velocity extrapolations. In order to find the optimum values of the suggested parameters, many numerical attempts are made. The numerical effects of both modified and current DTM procedures are compared. To validate the performance of the new algorithms, comparison studies are accomplished with the well-known time integration methods in solving some linear and nonlinear dynamic problems.