求解一维定常对流扩散反应方程的混合型紧致差分格式

借助显式紧致格式和隐式紧致格式的思想,基于截断误差余项修正,并结合原方程本身,构造出了一种求解一维定常对流扩散反应方程的高精度混合型紧致差分格式.格式仅用到三个点上的未知函数值及一阶导数值,而一阶导数值利用四阶Pade格式进行计算,格式整体具有四阶精度.数值实验结果验证了格式的精确性和可靠性.

Mixed High-order Compact Difference Scheme for Solving the Convection Diffusion Reaction Equation

With the help of explicit compact scheme and implicit compact scheme ideas,a mixed high-order compact difference scheme is constructed for solving the steady convection diffusion reaction problem.The scheme uses three-point unknown function values and theirs first-order derivative values.The first-order derivative is solved by the Padé scheme.The proposed scheme is overall fouth-order accuracy.the linear system arising from the scheme for Dirichlet boundary problem is tridiagonal.It can be solved by Thomas algorithm.Numerical experiments are given to prove the efficiency and dependability of the present scheme.