Zero-dissipative semi-implicit hybrid method for solving oscillatory or periodic problems

A Numerical Integrator for Oscillatory Problems

“…Hence, numerical techniques for obtaining approximate solution of the equations become the best option. A number of numerical methods for solving (1) have been proposed in the literature [2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24]1,25,26]. Some are direct while some are indirect methods.…”

“…To improve its properties for better performance, Ahmad et al [28] proposed semi-implicit hybrid methods up to algebraic order five. In the work of Jikantoro et al [1] it is pointed out that there is a huge advantage of improved accuracy and efficiency as the order of this method increases. Hence, we propose a semi-implicit hybrid method with higher algebraic order.…”

“…The problem of interest in this paper is an initial value problem (IVP) of the form: The importance of this problem cannot be over emphasized in science and engineering, as it arises in many areas including quantum mechanics, semi-discretizations of wave equation, astrophysics, electronics, celestial mechanics, quantum chemistry, molecular dynamics, and so on. For example, Schrödinger equation and many-body problem are oscillatory problems [1]. To validate models that exist in the form of (1), their solutions are of paramount importance.…”

Semi-implicit two-step hybrid method with FSAL property for solving second-order ordinary differential equations

“…There has been many research on multistep methods done for Eq. 1, particularly the two-step hybrid method (HM) (Tsitouras, 2003;Coleman, 2003;Franco, 2006;Fang and Wu, 2008;Samat et al, 2012;Ahmat et al, 2013;Jikantora et al, 2015;Franco et al, 2014;Franco and Randez, 2016;Kalogiratou et al, 2016). In a previous work, Coleman (2003), he has investigated the order condition of two-step hybrid method based on the theory of B-series.…”

“…The study by Ahmad et al (2013) developed semiimplicit two-step hybrid method up to algebraic order five for solving oscillatory problems by taking dispersion relation and solving them together with algebraic conditions of the methods. Later, another study carried out by Jikantora (2015) also developed semi-implicit two-step hybrid method with fifth algebraic order with dispersion and dissipation of higher order.…”