Efficient Finite Difference Methods for the Numerical Analysis of One-Dimensional Heat Equation
Efficient Finite Difference Methods for the Numerical Analysis of One-Dimensional Heat Equation作者机构：Department of Mathematics Comilla University Kotbari Bangladesh Department of Mathematical Sciences Kent State University Kent OH USA
出 版 物：《Journal of Applied Mathematics and Physics》 (应用数学与应用物理（英文）)
年 卷 期：2023年第11卷第10期
页 面：3099-3123页
学科分类：07[理学] 0701[理学-数学] 070101[理学-基础数学]
主 题：Explicit Scheme Implicit Scheme C-N Scheme CFL Condition
摘 要：In this paper, we investigate and analyze one-dimensional heat equation with appropriate initial and boundary condition using finite difference method. Finite difference method is a well-known numerical technique for obtaining the approximate solutions of an initial boundary value problem. We develop Forward Time Centered Space (FTCS) and Crank-Nicolson (CN) finite difference schemes for one-dimensional heat equation using the Taylor series. Later, we use these schemes to solve our governing equation. The stability criterion is discussed, and the stability conditions for both schemes are verified. We exhibit the results and then compare the results between the exact and approximate solutions. Finally, we estimate error between the exact and approximate solutions for a specific numerical problem to present the convergence of the numerical schemes, and demonstrate the resulting error in graphical representation.
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