Numerical Approximation of Heat Equation Using Haar Wavelets
نویسندگان
چکیده
Differential equations have several applications in several fields such as: physics, fluid dynamic and geophysics etc. However it is not always possible to get the solution in closed form and thus, numerical methods come into the picture. There are several numerical methods to handle a variety of problems: Finite Difference Method, Spectral Method, Finite Element Method, Finite Volume Method and so on. Many researchers are involved in developing various numerical schemes for finding solutions of different problems (see eg. [1, 2]). In this paper we consider one dimensional time-dependent heat conduction equation
منابع مشابه
Numerical solution of non-planar Burgers equation by Haar wavelet method
In this paper, an efficient numerical scheme based on uniform Haar wavelets is used to solve the non-planar Burgers equation. The quasilinearization technique is used to conveniently handle the nonlinear terms in the non-planar Burgers equation. The basic idea of Haar wavelet collocation method is to convert the partial differential equation into a system of algebraic equations that involves a ...
متن کاملAPPLICATION OF HAAR WAVELETS IN SOLVING NONLINEAR FRACTIONAL FREDHOLM INTEGRO-DIFFERENTIAL EQUATIONS
A novel and eective method based on Haar wavelets and Block Pulse Functions(BPFs) is proposed to solve nonlinear Fredholm integro-dierential equations of fractional order.The operational matrix of Haar wavelets via BPFs is derived and together with Haar waveletoperational matrix of fractional integration are used to transform the mentioned equation to asystem of algebraic equations. Our new met...
متن کاملSolving infinite horizon optimal control problems of nonlinear interconnected large-scale dynamic systems via a Haar wavelet collocation scheme
We consider an approximation scheme using Haar wavelets for solving a class of infinite horizon optimal control problems (OCP's) of nonlinear interconnected large-scale dynamic systems. A computational method based on Haar wavelets in the time-domain is proposed for solving the optimal control problem. Haar wavelets integral operational matrix and direct collocation method are utilized to find ...
متن کاملHaar Wavelet Method to Solve Volterra Integral Equations with Weakly Singular Kernel by Collocation Method
Volterra integral equations arise in many problems pertaining to mathematical physics like heat conduction problems. Several numerical methods for approximating the solution of Volterra integral equations are known [1-10]. This paper is focused on the solution of Volterra integral equations of the second kind with weakly singular kernel via Haar function by taking advantage of the nice properti...
متن کاملNUMERICAL SOLUTION OF LINEAR FREDHOLM AND VOLTERRA INTEGRAL EQUATION OF THE SECOND KIND BY USING LEGENDRE WAVELETS
In this paper, we use the continuous Legendre wavelets on the interval [0,1] constructed by Razzaghi M. and Yousefi S. [6] to solve the linear second kind integral equations. We use quadrature formula for the calculation of the products of any functions, which are required in the approximation for the integral equations. Then we reduced the integral equation to the solution of linear algebraic ...
متن کامل