Hicks, J.S. and Wei, J. (1967) Numerical Solution of Parabolic Partial Differential Equations with Two Point Boundary Conditions by Use of the Method of Lines. Journal of the ACM, 14, 549-562.
https://doi.org/10.1145/321406.321417

has been cited by the following article:

• TITLE: Solution of a One-Dimension Heat Equation Using Higher-Order Finite Difference Methods and Their Stability

  AUTHORS: M. Emran Ali, Wahida Zaman Loskor, Samia Taher, Farjana Bilkis

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

  JOURNAL NAME: Journal of Applied Mathematics and Physics, Vol.10 No.3, March 24, 2022

  ABSTRACT: 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.