Variable multistep methods
Variational iteration decomposition method for solving eighth-order boundary value problems.
Variational iteration method for fifth-order boundary value problems using He's polynomials.
Verification of functional a posteriori error estimates for obstacle problem in 1D
We verify functional a posteriori error estimate for obstacle problem proposed by Repin. Simplification into 1D allows for the construction of a nonlinear benchmark for which an exact solution of the obstacle problem can be derived. Quality of a numerical approximation obtained by the finite element method is compared with the exact solution and the error of approximation is bounded from above by a majorant error estimate. The sharpness of the majorant error estimate is discussed.
Verification of functional a posteriori error estimates for obstacle problem in 2D
We verify functional a posteriori error estimates proposed by S. Repin for a class of obstacle problems in two space dimensions. New benchmarks with known analytical solution are constructed based on one dimensional benchmark introduced by P. Harasim and J. Valdman. Numerical approximation of the solution of the obstacle problem is obtained by the finite element method using bilinear elements on a rectangular mesh. Error of the approximation is measured by a functional majorant. The majorant value...
Visualisation of the electromagnetic vector fields
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...
Well-posedness of the boundary value problem for parabolic equations in difference analogues of spaces of smooth functions.
Well-posedness of the difference schemes of the high order of accuracy for elliptic equations.
What do Multistep Methods Approximate?
Zero Dissipative DIRKN Pairs of Order 5(4) for Solving Special Second Order IVPs
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...
Zero-Stability Properties of the Three-Ordinate Variable Step-size Variable Formula Methods.
Zur Konvergenz von Näherungsverfahren bezüglich verschiedener Normen.
Zur Stabilität von Differenzenverfahren für Systeme linearer gewöhnlicher Randwertaufgaben.
Zur Struktur gewisser Konvergenzkriterien bei der numerischen Lösung von Anfangswertaufgaben.
Вариационно-сеточная аппроксимация
Вычисление инвариантов дифференциальных уравнений с помощью ЭВМ
Двухслойные разностные схемы для решения многоточечных задач
Дискретный вариант уравнения Ландау-Лифшица
К вопросу об аппроксимации функций собственными решениями двух задач Штурма-Лиувилля.
К теории вырожденных систем обыкновенных дифференциальных уравнений.