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A class of numerical solution of the parabolic equation Research and Application

Author: GeKun
Tutor: GuiBing
School: Nanjing Forestry University
Course: Applied Computer Technology
Keywords: Parabolic equation Difference Method Heat conduction equation Numerical solution
CLC: O241.82
Type: Master's thesis
Year: 2011
Downloads: 74
Quote: 0
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Abstract


Science and Engineering and the calculation , the study has a very practical application of the numerical solution of partial differential equations . For many difficult to obtain the exact solution of partial differential equations , numerical solution is obtained , and the port to take advantage of an important subject of research and practical application . Parabolic equation as an important part of the partial differential equations , numerical solution of the main object of this study . This paper first analyzes and discusses the three most widely used differential method , and stability analysis , combined with an instance of the one-dimensional heat conduction equation , using three differential method program , calculates its numerical solution and the many comparisons . Then raised three difference method based on a new weighted finite difference method for parabolic equations . Similarly, the paper also analyzed and discussed its stability , and combined with the instance of the one-dimensional heat conduction equation to calculate the numerical solution . Followed by comparison with the Crank-Nicolson method , indicating that this method has good accuracy . Finally, new differential unsteady heat conduction try to use the new method to solve the control equation of thermal conductivity , and the data obtained from the results of the analysis , results more in line with the actual problems , and achieved better results.

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CLC: > Mathematical sciences and chemical > Mathematics > Computational Mathematics > Numerical Analysis > The numerical solution of differential equations, integral equations > Numerical Solution of Partial Differential Equations
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