CAJ | 학술논문

对空间变量四阶紧致格式进行离散，时间变量保持不变，把一维对流扩散方程转化为常微分方程组的初值问题，再利用梯形方法构造对流扩散方程的时间二阶空间四阶精度的一种差分格式，并稳定性进行分析，数值结果与Crank-Nicholson 格式进行比较，数值结果表明，该方法可以很好地解决对流扩散方程的数值计算。
대공간변량사계긴치격식진행리산，시간변량보지불변，파일유대류확산방정전화위상미분방정조적초치문제，재이용제형방법구조대류확산방정적시간이계공간사계정도적일충차분격식，병은정성진행분석，수치결과여Crank-Nicholson 격식진행비교，수치결과표명，해방법가이흔호지해결대류확산방정적수치계산。
The compact finite difference approximation of fourth order was applied to discredit spatial de -rivatives but leave the time variable Continuous .This approach results in a system of ODEs , which can be used trapezoidal formula derived fourth order in space and second order in time unconditionally stable implicit scheme . The stability and local truncation error of the obtained method were analyzed Numerical experiments and com -pared with Crank -Nicolson scheme .Numerical experiments show that present method both stable and accurate approximations in exact solution , which is useful and efficient method for solving linear one dimensional convec-tion-diffusion equation .