differential equations

Application of Generalized Differential Quadrature Method to Two-dimensional Problems of Mechanics

Authors: Barulina M. A.
The application of the generalized differential quadrature method to the solution of two-dimensional problems of solid mechanics is discussed by an example of the sample analysis of vibrations o f a rectangular plate under various types of boundary cond itions. The dif ferential quadrature method (DQM) is known as an effective method for resolving differential equations, both ordinary an d partial.

Solution of Cauchy Problem for Equation First Order Via Haar Functions

Authors: Lukomskii D. S., Lukomskii S. F., Terekhin P. A.

In this article we consider a Cauchy problem for the first order differential equation and are looking for its numerical solution. For this aim we represent the derivative of the solution as Haar decomposition. We also obtain estimates of approximate solution. The method is computationally simple and applications are demonstrated through illustrative examples. These examples show that in some cases the error of the proposed method is much less, than in second order Runge – Kutta method.