The Experts below are selected from a list of 66 Experts worldwide ranked by ideXlab platform
Sławomir Milewski - One of the best experts on this subject based on the ideXlab platform.
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Meshless Finite Difference Method with Higher Order Approximation—Applications in Mechanics
Archives of Computational Methods in Engineering, 2012Co-Authors: Sławomir MilewskiAbstract:This work is devoted to some recent developments in the Higher Order Approximation introduced to the Meshless Finite Difference Method (MFDM), and its application to the solution of boundary value problems in mechanics. In the MFDM, approximation of the Sought Function is described in terms of nodes rather than by means of any imposed structure like elements, regular meshes etc. Therefore, the MFDM, using arbitrarily irregular clouds of nodes using the Moving Weighted Least Squares (MWLS) approximation falls into the category of the Meshless Methods (MM). The MFDM, dating to early seventies, is one of the oldest and possibly the most developed one. In this paper considered are some techniques which lead to improvement of the MFDM solution’s quality. The main objective of this paper is the presentation and overview of new ideas and the development of the Higher Order solution approach in the MFDM provided by correction terms, preceded by a brief information about the current state-of-the art of this method. The main concept of the Higher Order Approximation (HOA) used here, is based on consideration of additional terms in the local Taylor expansion of the Sought Function. It shall be demonstrated that such a move may essentially improve, in many ways, efficiency and solution quality of the Higher Order MFDM. The Higher Order correction terms may be applied in many aspects of the MFDM solution approach. Among them one may distinguish the a-posteriori error estimation as well as adaptive solution process with multigrid strategy. Moreover, in the present work considered are: computational implementation of the Higher Order MFDM algorithms, examination of the above mentioned aspects using 1D and 2D benchmark tests, as well as an application of the Higher Order MFDM solution approach to selected boundary value problems in mechanics.
Artur Krowiak - One of the best experts on this subject based on the ideXlab platform.
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Hermite type radial basis Function-based differential quadrature method for higher order equations
Applied Mathematical Modelling, 2016Co-Authors: Artur KrowiakAbstract:Abstract In the paper, the radial basis Function-based differential quadrature method (RBF-DQM) that uses Hermite type interpolation is developed. The method is an extension of the known RBF-DQM, which is a meshless numerical technique for solving differential equations. According to this technique, derivatives in a governing equation are approximated by a linear weighted sum of the Sought Function values defined at scattered nodes. To allow the method to be applied in higher order equations, where more than one boundary condition is imposed at an edge, Hermite type interpolation for the radial basis Functions is used and appropriate weighting coefficients for differential quadrature method are determined in the paper. As a numerical test the method is used to discretize the governing equation for the free vibration of thin plates with various boundary conditions. Different shaped plates with various boundary conditions are analyzed. The convergence tests carried out in the work confirm usefulness of the method as a truly meshless technique.
L. N. Bondarenko - One of the best experts on this subject based on the ideXlab platform.
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Finite-difference solution of a nonlinear initial-boundary-value problem for a nonlinear parabolic equation of second order
Journal of Soviet Mathematics, 1993Co-Authors: I. P. Gavrilyuk, P. F. Zhuk, L. N. BondarenkoAbstract:An implicit finite-difference scheme is constructed for solving a nonlinear initial-boundary-value problem for a nonlinear homogeneous parabolic equation of second order with a nonlinear boundary condition that contains the time derivative of the Sought Function. The results are used for numerical solution of the mathematical model of internal-diffusion kinetics of adsorption from a constant bounded volume .
Yuriy Povstenko - One of the best experts on this subject based on the ideXlab platform.
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axisymmetric solutions to fractional diffusion wave equation in a cylinder under robin boundary condition
European Physical Journal-special Topics, 2013Co-Authors: Yuriy PovstenkoAbstract:The axisymmetric time-fractional diffusion-wave equation with the Caputo derivative of the order 0 < α ≤ 2 is considered in a cylinder under the prescribed linear combination of the values of the Sought Function and the values of its normal derivative at the boundary. The fundamental solutions to the Cauchy, source, and boundary problems are investigated. The Laplace transform with respect to time and finite Hankel transform with respect to the radial coordinate are used. The solutions are obtained in terms of Mittag-Leffler Functions. The numerical results are illustrated graphically.
O. V. Drozhzhina - One of the best experts on this subject based on the ideXlab platform.
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The Inverse Problem for Numerical Determination of the Nonlinear Right-Hand Side in a Parabolic Equation
Computational Mathematics and Modeling, 2003Co-Authors: O. V. DrozhzhinaAbstract:The article considers the inverse problem of determining the nonlinear right-hand side of a quasi-linear parabolic equation and proves a uniqueness theorem. A method is proposed for numerical solution of the inverse problem based on parametric representation of the Sought coefficient. The inverse problem thus reduces to finding the error-minimizing vector of unknown coefficients of the parametric representation of the Sought Function.