Least-squares differential quadrature time integration scheme in the dual reciprocity boundary element method solution of diffusive-convective problems

Least-squares differential quadrature method (DQM) is used for solving the ordinary differential equations in time, obtained from the application of dual reciprocity boundary element method (DRBEM) for the spatial partial derivatives in diffusive-convective type problems with variable coefficients. The DRBEM enables us to use the fundamental solution of Laplace equation, which is easy to implement computation ally. The terms except the Laplacian are considered as the nonhomogeneity in the equation, which are approximated in terms of radial basis functions. The application of DQM for time derivative discretization when it is combined with the DRBEM gives an overdetermined system of linear equations since both boundary and initial conditions are imposed. The least squares approximation is used for solving the overdetermined system. Thus, the solution is obtained at any time level without using an iterative scheme. Numerical results are in good agreement with the theoretical solutions of the diffusive-convective problems considered.


Dynamic programming for a Markov-switching jump-diffusion
Azevedo, N.; Pinheiro, D.; Weber, Gerhard Wilhelm (Elsevier BV, 2014-09-01)
We consider an optimal control problem with a deterministic finite horizon and state variable dynamics given by a Markov-switching jump-diffusion stochastic differential equation. Our main results extend the dynamic programming technique to this larger family of stochastic optimal control problems. More specifically, we provide a detailed proof of Bellman's optimality principle (or dynamic programming principle) and obtain the corresponding Hamilton-Jacobi-Belman equation, which turns out to be a partial in...
DBEM and DRBEM solutions to 2D transient convection-diffusion-reaction type equations
Fendoglu, Hande; Bozkaya, Canan; Tezer, Münevver (Elsevier BV, 2018-08-01)
The present study focuses on the numerical solution of the transient convection-diffusion-reaction equation by transforming it into modified Helmholtz equation through an exponential type transformation. In the spatial discretization of the problem domain two different boundary element methods (BEM), namely the domain BEM (DBEM) and the dual reciprocity BEM (DRBEM), are employed which are combined with an implicit backward finite difference time integration. The BEM techniques differ in the sense of treatin...
DRBEM solution of exterior nonlinear wave problem using FDM and LSM time integrations
Meral, Guelnihal; Tezer, Münevver (Elsevier BV, 2010-06-01)
The nonlinear wave equation is solved numerically in an exterior region For the discretization of the space derivatives dual reciprocity boundary element method (DRBEM) is applied using the fundamental solution of Laplace equation. The time derivative and the nonlinearity are treated as the nonhomogenity. The boundary integrals coming from the far boundary are eliminated using rational and exponential interpolation functions which have decay properties far away from the region of Interest. The resulting sys...
On Stability of Linear Delay Differential Equations under Perron's Condition
Diblík, J.; Zafer, A. (Hindawi Limited, 2011)
The stability of the zero solution of a system of first-order linear functional differential equations with nonconstant delay is considered. Sufficient conditions for stability, uniform stability, asymptotic stability, and uniform asymptotic stability are established.
Error estimates for space-time discontinuous Galerkin formulation based on proper orthogonal decomposition
Akman, Tuğba (Informa UK Limited, 2017-01-01)
In this study, proper orthogonal decomposition (POD) method is applied to diffusion-convection-reaction equation, which is discretized using spacetime discontinuous Galerkin (dG) method. We provide estimates for POD truncation error in dG-energy norm, dG-elliptic projection, and spacetime projection. Using these new estimates, we analyze the error between the dG and the POD solution, and the error between the exact and the POD solution. Numerical results, which are consistent with theoretical convergence ra...
Citation Formats
C. Bozkaya, “Least-squares differential quadrature time integration scheme in the dual reciprocity boundary element method solution of diffusive-convective problems,” ENGINEERING ANALYSIS WITH BOUNDARY ELEMENTS, pp. 83–93, 2007, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/44787.