SavedAdd your journal

Journals / Sigma Mühendislik ve Fen Bilimleri Dergisi / 2020 / Cilt: 38 - Sayı: 1

Application of crank-nicolson method to a random component heat equation

Halil ANAÇ
Mehmet MERDAN
Tülay KESEMEN
Pages
475–480
Publication Date
2020-03-27
DOI
—
🏛️Bibliographic metadata and full text access for this article are provided via DergiPark.
DergiPark Record ↗
✨

AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

Firstly, a random component heat equation is solved by this method.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:In this study, the solution of a random component heat equation is obtained by using Crank-Nicolson Method.
📊
Key Findings & Data:The initial condition of this equation is examined by Normal distribution.
💡
Conclusion & Impact:Firstly, a random component heat equation is solved by this method.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Random component heat equation · expected value · Crank-Nicolson method

Abstract

In this study, the solution of a random component heat equation is obtained by using Crank-Nicolson Method. The initial condition of this equation is examined by Normal distribution. The expected value and variance of solution of this equation are obtained. Crank-Nicolson method is applied to analyze the solution of this equation. Also, the solution and the graphs of the expected value and variance are obtained by using MATLAB software. The results of the heat equation are compared with random characteristics of this equation. Firstly, a random component heat equation is solved by this method.

🔖

Cite This Article

ANAÇ, H., MERDAN, M., KESEMEN, T. (2020). Application of crank-nicolson method to a random component heat equation. Sigma Mühendislik ve Fen Bilimleri Dergisi, Cilt: 38 - Sayı: 1, 475–480. https://ajindex.com/articles/419317

📄 Full Text PDF Viewer

📄

PDF görüntüleyici hazırlanıyor...

References (15)

  1. Ayaz, F. (2004). Solutions of the system of differential equations by differential transform method. Applied Mathematics and Computation, 147(2), 547-567
  2. Babuška, I., Nobile, F., & Tempone, R. (2007). A stochastic collocation method for elliptic partial differential equations with random input data. SIAM Journal on Numerical Analysis, 45(3), 1005-1034
  3. Charrier, J. (2012). Strong and weak error estimates for elliptic partial differential equations with random coefficients. SIAM Journal on numerical analysis, 50(1), 216-246
  4. Crank, J., & Nicolson, P. (1947). A practical method for numerical evaluation of solutions of partial differential equations of the heat conduction type. Proc. Camb. Phil. Soc., 43(1), 50-67, doi:10.1007/BF02127704
  5. Cortés, J.C., Jódar, L., Villafuerte, L., & Villanueva, R.J. (2007). Computing mean square approximations of random diffusion models with source term. Mathematics and Computers in Simulation, 76(1-3), 44-48
  6. Çelik, C., & Duman, M. (2012). Crank–Nicolson method for the fractional diffusion equation with the Riesz fractional derivative, Journal of computational physics, 231(4), 1743-1750
  7. Ekolin, G. (1991). Finite difference methods for a nonlocal boundary value problem for the heat equation. BIT 31, 245-261
  8. El-Tawil, & Sohaly, M.A. (2012). Mean square convergent three points finite difference scheme for random partial differential equations. J. of the Egyptian Math. Soc., 20(3), 188-204
  9. Feller, W. (2008). An introduction to probability theory and its applications (Vol. 2). John Wiley & Sons
  10. Gunzburger, M. D., Webster, C. G., & Zhang, G. (2014). Stochastic finite element methods for partial differential equations with random input data. Acta Numerica, 23, 521-650
  11. He, J.H. (1999). Variational iteration method-a kind of non-linear analytical technique:some examples. Int. J. of Non-Linear Mech., 34(4), 699-708
  12. He, J.H. (2003). Homotopy perturbation method: a new nonlinear analytical technique. Applied Mathematics and computation, 135(1), 73-79
  13. He, J.H. (2006). Homotopy perturbation method for solving boundary value problems. Physics letters A, 350(1-2), 87-88
  14. He, J.H. (2006). Addendum: new interpretation of homotopy perturbation method. International Journal of Modern Physics B, 20(18), 2561-2568
  15. Kangalgil, F., & Ayaz, F. (2009). Solitary wave solutions for the KdV and mKdV equations by differential transform method. Chaos, Solitons & Fractals, 41(1), 464-