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References in periodicals archive ?
(2016) extended the work of Hamad by incorporating a thermal radiation parameter into the flow equations and solved them using the Runge-kutta Fehlberg method together with shooting technique.
In [28], we proposed the approximate Prediction-Based Control (aPBC) with a methodology based on the implicit Runge-Kutta method and state estimation applied to predict future states for the free system in real time based on system model.
This work deals with exponentially fitted and trigonometrically fitted modified Runge-Kutta type methods for solving third-order ordinary differential equations (ODEs)
Methods such as Runge-Kutta (RK), Runge-Kutta Nystrom (RKN), hybrid, and multistep are widely used for solving DDEs.
For DAEs in general, the most popular one-step methods are implicit Runge-Kutta (IRK) methods, which are stiffly accurate; see [8, 10, 13, 15].
The integration of the temporal domain was conducted using an explicit fourth-order Runge-Kutta [17].
Numerical solutions are presented via trapezoidal rule for the objective functional and Euler method and fourth-order Runge-Kutta method for solving uncertain differential equations due to its ability to yield more precise outcomes than other methods for the constraints, Yang and Shen [24].
Runge-Kutta method was extensively used for solving the different model of corrosion.
In such cases, the most widely used time-discretizations are the special organized numerical methods, such as the implicit-explicit numerical methods [6, 7], the additive Runge-Kutta methods [8-12], and the linearized methods [13, 14].
The equation of motion that is representing dynamic behaviour is integrated by using the fourth-order Runge-Kutta method.
For K(x, s) = 1, Runge-Kutta method is involved in solving differential part of VIDE, while, midpoint method is needed to solve VIDE when K(x, s) [not equal to] 1.