Balancing of Diffusion Partial Differential Equation
نویسنده
چکیده
This paper concerns with the balancing theory for the system governed by diffusion partial differential equation, which is refereed here as infinite dimensional system or distributed-parameter system. Based on the eigenvalue-eigenfunction structure of Laplacian differential operator, the approximate controllability and initial observability are constructed. In order to perform the balanced realization for infinite dimensional system, a brief review on finite dimensional balancing is presented, and more intuitive meaning of balanced realization is then obtained. After defining the Hankel operator of the infinite dimensional system, we compute the Hankel singular value and construct the energy balancing. And then, the model reduction problem is discussed. In the sequel, numerical simulation of the balanced model reduction for one-dimensional heat equation is conducted. Ke)"vords: Hankel singular value, balancing theory, diffusion system, infinite dimensional system, distributed parameter system.
منابع مشابه
A Diffusion Equation with Exponential Nonlinearity Recant Developments
The purpose of this paper is to analyze in detail a special nonlinear partial differential equation (nPDE) of the second order which is important in physical, chemical and technical applications. The present nPDE describes nonlinear diffusion and is of interest in several parts of physics, chemistry and engineering problems alike. Since nature is not linear intrinsically the nonlinear case is t...
متن کاملNumerical Solution of Caputo-Fabrizio Time Fractional Distributed Order Reaction-diffusion Equation via Quasi Wavelet based Numerical Method
In this paper, we derive a novel numerical method to find out the numerical solution of fractional partial differential equations (PDEs) involving Caputo-Fabrizio (C-F) fractional derivatives. We first find out the approximation formula of C-F derivative of function tk. We approximate the C-F derivative in time with the help of the Legendre spectral method and approximation formula o...
متن کاملSpace-time radial basis function collocation method for one-dimensional advection-diffusion problem
The parabolic partial differential equation arises in many application of technologies. In this paper, we propose an approximate method for solution of the heat and advection-diffusion equations using Laguerre-Gaussians radial basis functions (LG-RBFs). The results of numerical experiments are compared with the other radial basis functions and the results of other schemes to confirm the validit...
متن کاملA numerical method for solving a class of distributed order time-fractional diffusion partial differential equations according to Caputo-Prabhakar fractional derivative
In this paper, a time-fractional diffusion equation of distributed order including the Caputo-Prabhakar fractional derivative is studied. We use a numerical method based on the linear B-spline interpolation and finite difference method to study the solutions of these types of fractional equations. Finally, some numerical examples are presented for the performance and accuracy of the proposed nu...
متن کاملFinite integration method with RBFs for solving time-fractional convection-diffusion equation with variable coefficients
In this paper, a modification of finite integration method (FIM) is combined with the radial basis function (RBF) method to solve a time-fractional convection-diffusion equation with variable coefficients. The FIM transforms partial differential equations into integral equations and this creates some constants of integration. Unlike the usual FIM, the proposed method computes constants of integ...
متن کامل