Crank-Nicolson and Modified Crank-Nicolson Scheme for One Dimensional Parabolic Equation
International Journal of Applied Mathematics and Theoretical Physics
Volume 6, Issue 3, September 2020, Pages: 35-40
Received: May 28, 2020; Accepted: Jul. 13, 2020; Published: Aug. 13, 2020
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Omowo Babajide Johnson, Department of Mathematics, Nasarawa State University, Keffi, Nigeria
Longe Idowu Oluwaseun, Department of Statistics, Federal Polytechnic, Ile-Oluji, Nigeria
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Partial differential equations are very important tools for mathematical modeling in some field like; physics, engineering and applied Mathematics. It’s worth knowing that only few of this equation can be solved analytically and numerical method have been proven to perform exceedingly well in solving even difficult partial differential equations. Finite difference method is a popular numerical method which has been applied extensively to solve partial differential equations. A well known type of this method is the Classical Crank-Nicolson scheme which has been used by different researchers. In this work, we present a modified Crank-Nicolson scheme resulting from the modification of the classical Crank-Nicolson scheme to solve one dimensional parabolic equation. We apply both the Classical Crank-Nicolson scheme and the modified Crank-Nicolson scheme to solve one dimensional parabolic partial differential equation and investigate the results of the different schemes. The computation and results of the two schemes converges faster to the exact solution. It is shown that the modified Crank-Nicolson method is more efficient, reliable and better for solving Parabolic Partial differential equations since it requires less computational work. The method is stable and the convergence is fast when the results of the numerical examples where compared with the results from other existing classical scheme, we found that our method have better accuracy than those methods. Some numerical examples were considered to verify our results.
Finite Difference Method, Parabolic Equation, Crank-Nicolson Scheme, Modified Crank-Nicolson Method, Stability
To cite this article
Omowo Babajide Johnson, Longe Idowu Oluwaseun, Crank-Nicolson and Modified Crank-Nicolson Scheme for One Dimensional Parabolic Equation, International Journal of Applied Mathematics and Theoretical Physics. Special Issue: Computational Mathematics. Vol. 6, No. 3, 2020, pp. 35-40. doi: 10.11648/j.ijamtp.20200603.11
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