Combining modified integral quadrature method with simulation technique to solve nonlinear initial and boundary value problems

Abstract

Most ordinary differential equations (ODEs) can be solved using simulation technique (ST), which, however, requires the enforcement of conditions at any time domain, this limitation is the main drawback. Another numerical method, the differential quadrature method (DQM) or the integral quadrature method (IQM), leads to very accurate results using only a few grids on the domain, which, however, is not flexible for nonlinear ODEs and is not easy to impose multiple conditions on the same location. For these reasons, ST is combined with IQM to eliminate the mentioned disadvantages of the ST and IQM. Numerical examples (nonlinear vibration and boundary value problems) showed good agreements when compared with other works.