Solution of singular and nonsingular initial and boundary value problems by modified variational iteration method.
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Noor, Muhammad Aslam, Mohyud-Din, Syed Tauseef (2008)
Mathematical Problems in Engineering
Mohsen Mehrali-Varjani, Mostafa Shamsi, Alaeddin Malek (2018)
Kybernetika
This paper presents a numerical approach to solve the Hamilton-Jacobi-Bellman (HJB) problem which appears in feedback solution of the optimal control problems. In this method, first, by using Chebyshev pseudospectral spatial discretization, the HJB problem is converted to a system of ordinary differential equations with terminal conditions. Second, the time-marching Runge-Kutta method is used to solve the corresponding system of differential equations. Then, an approximate solution for the HJB problem...
David J. Knezevic, Endre Süli (2009)
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
This paper is concerned with the analysis and implementation of spectral Galerkin methods for a class of Fokker-Planck equations that arises from the kinetic theory of dilute polymers. A relevant feature of the class of equations under consideration from the viewpoint of mathematical analysis and numerical approximation is the presence of an unbounded drift coefficient, involving a smooth convex potential that is equal to along the boundary of the computational domain . Using a symmetrization...
David J. Knezevic, Endre Süli (2008)
ESAIM: Mathematical Modelling and Numerical Analysis
This paper is concerned with the analysis and implementation of spectral Galerkin methods for a class of Fokker-Planck equations that arises from the kinetic theory of dilute polymers. A relevant feature of the class of equations under consideration from the viewpoint of mathematical analysis and numerical approximation is the presence of an unbounded drift coefficient, involving a smooth convex potential U that is equal to +∞ along the boundary ∂D of the computational domain D. Using a symmetrization...
Pech, Jan (2021)
Programs and Algorithms of Numerical Mathematics
This work presents simulations of incompressible fluid flow interacting with a moving rigid body. A numerical algorithm for incompressible Navier-Stokes equations in a general coordinate system is applied to two types of body motion, prescribed and flow-induced. Discretization in spatial coordinates is based on the spectral/hp element method. Specific techniques of stabilisation, mesh design and approximation quality estimates are described and compared. Presented data show performance of the solver...
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