Du Fort-frankel Difference Scheme For Solving The Three-dimensional Diffusion Equation

The initial and fringe value question for the diffusion question was the nonrepresentational mathematic model from physics,chemistry,dynamics , people have interest in study its difference scheme . because of the diffusion equation's spread and application , there was a lot of method for the diffusion equation , they have important theoretic and actual meaning for the math . This paper mostly work over the Du Fort-Frankel difference scheme for the three-dimensional diffusion equation , and construct the difference scheme have high precision and unconditional stabilization , as well as give the relevant numerical example and validate the correctness for the theoretic analysis . This paper use for reference the pre-human method , use the finite difference method construct the Du Fort-Frankel difference scheme for the three-dimensional diffusion equation , and use the multidimensional Taylor formula work out the truncation error for the difference scheme . Make use of the most model theorem analyze the scheme's stability , and we receive that the scheme is unconditional stability . In this paper the precision for the diffusion equation difference scheme is better than the former for the half explicit scheme and intimacy scheme . This paper's scheme is explicit in the calculate , and the numeration is convenient , simple , fast and the efficiency is supernal. Then we introduce cyber-arithmetic for the difference scheme and give the numerical example . About the difference scheme we write the arithmetic in Matlab , and validate the theoretic result use numerical example . In the end summarize what the paper have did , such as the precision stability and practicability for the difference in order to construct the high and complicated difference scheme about the partial differential equation .