ZHAN Yong-qiang, ZHANG Chuan-lin. A Family of High Accuracy Implicit Difference Schemes for Solving Parabolic Equations[J]. Applied Mathematics and Mechanics, 2014, 35(7): 790-797. doi: 10.3879/j.issn.1000-0887.2014.07.008
Citation: ZHAN Yong-qiang, ZHANG Chuan-lin. A Family of High Accuracy Implicit Difference Schemes for Solving Parabolic Equations[J]. Applied Mathematics and Mechanics, 2014, 35(7): 790-797. doi: 10.3879/j.issn.1000-0887.2014.07.008

A Family of High Accuracy Implicit Difference Schemes for Solving Parabolic Equations

doi: 10.3879/j.issn.1000-0887.2014.07.008
Funds:  The National Natural Science Foundation of China(61070165)
  • Received Date: 2014-01-16
  • Rev Recd Date: 2014-05-15
  • Publish Date: 2014-07-15
  • A family of implicit difference schemes with high accuracy for solving 1-dimensional parabolic equations were given. First, a difference approximation expression of the first order partial derivative of the solution to the parabolic equation was deduced at the special nodes; then this difference approximation expression and the second order central difference quotient approximation were used to construct a family of implicit difference schemes by the method of undetermined coefficients, and appropriate parameters were chosen to endow the schemes with high order truncation errors. In turn, the new difference schemes were proved to be stable as long as r was more than 1/6 with the Fourier analysis method. Finally, a numerical experiment was conduted on comparison of accuracy between the exact solutions, results of the new difference schemes and those of the other schemes with the same order truncation errors, as well as comparison of computational efficiency between the new schemes and the classical implicit difference schemes. The results demonstrate the high accuracy and efficiency of the presented difference schemes.
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