Various issues related to the development of a new code for nonstiff differential equations are discussed. This code is based on two-step Runge-Kutta methods of order five and stage order five. Numerical experiments are presented which demonstrate that the new code is competitive with the Matlab ode45 program for all tolerances.
This work deals with the flow of incompressible viscous fluids in a two-dimensional branching channel. Using the immersed boundary method, a new finite difference solver was developed to interpret the channel geometry. The numerical results obtained by this new solver are compared with the numerical simulations of the older finite volume method code and with the results obtained with OpenFOAM. The aim of this work is to verify whether the immersed boundary method is suitable for fluid flow in channels...
Modern computer algebra software can be used to visualize vector fields. One of the most used is the Maple program. This program is used to visualize two and three-dimensional vector fields. The possibilities of plotting direction vectors, lines of force, equipotential curves and the method of colouring the surface area for two-dimensional cases are shown step by step. For three-dimensional arrays, these methods are applied to various slices of three-dimensional space, such as a plane or a cylindrical...
For initial value problem (IVPs) in ordinary second order differential equations of the special form possessing oscillating solutions, diagonally implicit Runge–Kutta–Nystrom (DIRKN) formula-pairs of orders 5(4) in 5-stages are derived in this paper. The method is zero dissipative, thus it possesses a non-empty interval of periodicity. Some numerical results are presented to show the applicability of the new method compared with existing Runge–Kutta (RK) method applied to the problem reduced to...