Author(s)

M. Emran Ali¹, Wahida Zaman Loskor², Samia Taher², Farjana Bilkis²

¹Department of Textile Engineering, Northern University Bangladesh, Dhaka, Bangladesh.
²Department of Science and Humanities, Bangladesh Army International University of Science & Technology, Cumilla, Bangladesh.

One-dimensional heat equation was solved for different higher-order finite difference schemes, namely, forward time and fourth-order centered space explicit method, backward time and fourth-order centered space implicit method, and fourth-order implicit Crank-Nicolson finite difference method. Higher-order schemes have complexity in computing values at the neighboring points to the boundaries. It is required there a specification of the values of field variables at some points exterior to the domain. The complexity was incorporated using Hicks approximation. The convergence and stability analysis was also computed for those higher-order finite difference explicit and implicit methods in case of solving a one dimensional heat equation. The obtained numerical results were compared with exact solutions. It is found that backward time and fourth-order centered space implicit scheme along with Hicks approximation performed well over the other mentioned higher-order approaches.

Heat Equation, Boundary Condition, Higher-Order Finite Difference Methods, Hicks Approximation

Ali, M. , Loskor, W. , Taher, S. and Bilkis, F. (2022) Solution of a One-Dimension Heat Equation Using Higher-Order Finite Difference Methods and Their Stability. Journal of Applied Mathematics and Physics, 10, 877-886. doi: 10.4236/jamp.2022.103060.