Explicit Difference Methods for Solving the Cylindrical Heat Conduction Equation

Explicit Difference Methods for Solving the Cylindrical Heat Conduction Equation

? = 0(r = 0), i^=-F(i), (r=l) dr u dr where Fit) is an empirical function of t. In all cases, as far as the authors are aware, the differential coefficients in (1) are considered separately when replaced by differences, and the principal term in du the truncation error of any difference formula obtained in this way contains — and ö u —Z-. This can be seen by obtaining the time derivatives of u ...

A Finite Difference Scheme for the Heat Conduction Equation

We use equations similar to the heat conduction equation to calulate heat transfer, radiation transfer and hydrostatical equilibrium in our stellar evolution programs. We tried various numerical schemes and found that the most convenient scheme for complicated calculations (nonlinear, multidimensional calculations) is a symmetrical semi-implicit (SSI) scheme. The (SSI) scheme is easy to code, v...

Two numerical methods for solving a backward heat conduction problem

We introduce a central difference method and a quasi-reversibility method for solving a backward heat conduction problem (BHCP) numerically. For these two numerical methods, we give the stability analysis. Meanwhile, we investigate the roles of regularization parameters in these two methods. Numerical results show that our algorithm is effective. 2005 Elsevier Inc. All rights reserved.

Wavelet and Fourier Methods for Solving the Sideways Heat Equation

We consider an inverse heat conduction problem, the Sideways Heat Equation, which is a model of a problem, where one wants to determine the temperature on both sides of a thick wall, but where one side is inaccessible to measurements. Mathematically it is formulated as a Cauchy problem for the heat equation in a quarter plane, with data given along the line x = 1, where the solution is wanted f...

The use of iterative methods for solving Black-Scholes equation