On the solution of one-dimensional heat equation with higher-order non-central finite difference method of lines

  • Gour Chandra Paul Department of Mathematics, University of Rajshahi, Rajshahi 6205, Bangladesh
  • Md. Emran Ali Department of Textile Engineering, Northern University Bangladesh, Dhaka 1230, Bangladesh


In this paper, a one-dimensional heat equation with Dirichlet boundary condition is solved using the method of lines where the discretization is made with the help of higher-order noncentral finite difference approximation method. During imposing higher-order approximation method, the specification of the values of the field variable at some exterior points outside the domain are required which are made using proper assumption. It is found that the attained results agree well with the exact solution on the basis of the root mean square errors.


Ahmad, R.R. and Yaacob, N., 2013. Arithmetic-mean Runge-Kutta method and method of lines for solving mildly stiff differential equations, Menemui Matematik (Discovering Mathematics),
35(2), 21-29.
Ashino, R., Nagase, M. and Vaillancourt, R. (2000), Behind and beyond the MATLAB ODE suite, Comput. Math. with Appl., 40(4-5): 491-512.
Bakodah, H. (2011), Non-central 7-point formula in method of lines for parabolic and Burger’s equation. IJRRAS 8: 328-336.
Butcher, J.C. (2016), Numerical methods for ordinary differential equations, John Wiley & Sons.
Chapra, S.C. and Canale, R.P. (2015), Numerical Methods for Engineers (Seventh edition), McGrawHill Education.
Hicks, J.S., Wei, J. (1967), Numerical solution of parabolic partial differential equations with two point boundary conditions by use of the method of lines. JACM 14(3): 549-562.
Paul, G.C., Ismail, A.I.M., Karim, M.F. (2014), Implementation of method of lines to predict water levels due to a storm along the coastal region of Bangladesh. J. Oceanogr, 70(3): 199-210.
Paul, G.C., Senthilkumar, S. and Pria, R. (2018), Storm surge simulation along the Meghna estuarine area: an alternative approach, Acta Oceanol. Sin., 37(1): 40-49.
Paul, G.C. and Ali, M.E. (2019), Solution of one-dimensional heat equation: An alternative approach, Menemui Matematik (Discovering Mathematics), 41(1), 22-33.
Pregla, R. (1987), About the nature of the method of lines, AEU Archiv für Elektronik und Übertragungstechnik, 41(6): 368-370.
Pregla, R. and Pascher, W. (1989), The method of lines numerical techniques for micro-wave and millimeter-wave passive structure, John Wiley, New York: 381-446.
Sadiku, M.N.O. and Obiozor, C.N. (2000), A simple introduction to the method of lines, Int. J. Electr. Eng. Educ., 37(3): 282-296.
Schiesser, W.E. and Griffiths, G.W. (2009), A compendium of partial differential equation models: method of lines analysis with Matlab, Cambridge University Press.
Tadmor, E. (2012), A review of numerical methods for nonlinear partial differential equations. B. Am. Math. Soc., 49 (4): 507-554
How to Cite
PAUL, Gour Chandra; ALI, Md. Emran. On the solution of one-dimensional heat equation with higher-order non-central finite difference method of lines. Menemui Matematik (Discovering Mathematics), [S.l.], v. 45, n. 2, p. 200-207, nov. 2023. ISSN 0126-9003. Available at: <https://myjms.mohe.gov.my/index.php/dismath/article/view/24754>. Date accessed: 26 july 2024.

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