A High-order Implicit Difference Method for the One-dimensional Convection Diffusion Equation
نویسندگان
چکیده
Based on the exponent transform to eliminate the “convection item” in the equation and the fourth-order compact difference formulas for the first and second derivatives, two chasses of new implicit difference schemes are proposed for solving the one-dimensional convection-diffusion equation. The methods are of order O ( τ2 + h4 ) and O ( τ4 + h4 ) respectively. The former is proved to be unconditionally stable while the later is unconditionally unstable by Fourier analysis. The result of numerical experiment shows that the O ( τ2 + h4 ) scheme is an effective difference scheme to solve the convection diffusion problem.
منابع مشابه
An Implicit Difference-ADI Method for the Two-dimensional Space-time Fractional Diffusion Equation
Fractional order diffusion equations are generalizations of classical diffusion equations which are used to model in physics, finance, engineering, etc. In this paper we present an implicit difference approximation by using the alternating directions implicit (ADI) approach to solve the two-dimensional space-time fractional diffusion equation (2DSTFDE) on a finite domain. Consistency, unconditi...
متن کاملA Fourth-Order Compact Finite Difference Scheme for Solving Unsteady Convection-Diffusion Equations
Convection-diffusion equations are widely used for modeling and simulations of various complex phenomena in science and engineering (Hundsdorfer & Verwer, 2003; Morton, 1996). Since for most application problems it is impossible to solve convection-diffusion equations analytically, efficient numerical algorithms are becoming increasingly important to numerical simulations involving convection-d...
متن کاملA New Implicit Finite Difference Method for Solving Time Fractional Diffusion Equation
In this paper, a time fractional diffusion equation on a finite domain is con- sidered. The time fractional diffusion equation is obtained from the standard diffusion equation by replacing the first order time derivative by a fractional derivative of order 0 < a< 1 (in the Riemann-Liovill or Caputo sence). In equation that we consider the time fractional derivative is in...
متن کاملThe streamline diffusion method with implicit integration for the multi-dimensional Fermi Pencil Beam equation
We derive error estimates in the appropriate norms, for the streamlinediffusion (SD) finite element methods for steady state, energy dependent,Fermi equation in three space dimensions. These estimates yield optimal convergencerates due to the maximal available regularity of the exact solution.High order SD method together with implicit integration are used. The formulationis strongly consistent...
متن کاملAn alternating direction implicit method for a second-order hyperbolic diffusion equation with convection
A numerical method is presented to solve a two-dimensional hyperbolic diffusion problem where is assumed that both convection and diffusion are responsible for flow motion. Since direct solutions based on implicit schemes for multidimensional problems are computa-tionally inefficient, we apply an alternating direction method which is second order accurate in time and space. The stability of the...
متن کامل