Numerical Solution of Physics-based Models by Functional Transformations
نویسنده
چکیده
Various image processing algorithms can be related to physical models described by partial diierential equations. The traditional way for their numerical solution are nite diierences and nite elements. However, the application of methods from multidimensional systems theory and digital signal processing opens new ways for the eecient simulation of time and space dependent problems like wave propagation or heat and mass transfer. The basic idea is the application of suitably chosen functional transformations for the time and space coordinates. Initial and boundary conditions are considered in a systematic way. This leads to the structure of a discrete system which closely models the behaviour of the given continuous system and which is suitable for computer implementation.
منابع مشابه
Using Chebyshev polynomial’s zeros as point grid for numerical solution of nonlinear PDEs by differential quadrature- based radial basis functions
Radial Basis Functions (RBFs) have been found to be widely successful for the interpolation of scattered data over the last several decades. The numerical solution of nonlinear Partial Differential Equations (PDEs) plays a prominent role in numerical weather forecasting, and many other areas of physics, engineering, and biology. In this paper, Differential Quadrature (DQ) method- based RBFs are...
متن کاملNumerical Solution of Weakly Singular Ito-Volterra Integral Equations via Operational Matrix Method based on Euler Polynomials
Introduction Many problems which appear in different sciences such as physics, engineering, biology, applied mathematics and different branches can be modeled by using deterministic integral equations. Weakly singular integral equation is one of the principle type of integral equations which was introduced by Abel for the first time. These problems are often dependent on a noise source which a...
متن کاملNumerical solution of functional integral equations by using B-splines
This paper describes an approximating solution, based on Lagrange interpolation and spline functions, to treat functional integral equations of Fredholm type and Volterra type. This method can be extended to functional differential and integro-differential equations. For showing efficiency of the method we give some numerical examples.
متن کاملSymplectic and symmetric methods for the numerical solution of some mathematical models of celestial objects
In the last years, the theory of numerical methods for system of non-stiff and stiff ordinary differential equations has reached a certain maturity. So, there are many excellent codes which are based on Runge–Kutta methods, linear multistep methods, Obreshkov methods, hybrid methods or general linear methods. Although these methods have good accuracy and desirable stability properties such as A...
متن کاملNumerical solution of the spread of infectious diseases mathematical model based on shifted Bernstein polynomials
The Volterra delay integral equations have numerous applications in various branches of science, including biology, ecology, physics and modeling of engineering and natural sciences. In many cases, it is difficult to obtain analytical solutions of these equations. So, numerical methods as an efficient approximation method for solving Volterra delay integral equations are of interest to many res...
متن کامل