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A Numerical Solution of Heat Equation for Several Thermal Diffusivity Using Finite Difference Scheme with Stability Conditions

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Journal of Applied Mathematics and Physics 2022年第2期10卷 449-465页

作者： wahida zaman loskor Rama Sarkar Department of Science and Humanities Bangladesh Army International University of Science and Technology Cumilla Bangladesh Department of Mathematics and Statistics Bangladesh University of Business and Technology Dhaka Bangladesh

The heat equation is a second-order parabolic partial differential equation, which can be solved in many ways using numerical methods. This paper provides a numerical solution that uses the finite difference method like the explicit center difference method. The forward time and centered space (FTCS) is used to a problem containing the one-dimensional heat equation and the stability condition of the scheme is reported with different thermal conductivity of different materials. In this study, results obtained for different thermal conductivity of distinct materials are compared. Also, the results reveal the well-behavior properties of the materials in good agreement.

关键词： Heat Equation Finite-Difference Scheme Explicit Centered Difference Scheme Thermal Diffusivity

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

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Journal of Applied Mathematics and Physics 2022年第3期10卷 877-886页

作者： M. Emran Ali wahida zaman loskor Samia Taher Farjana Bilkis Department of Textile Engineering Northern University Bangladesh Dhaka Bangladesh Department 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.

关键词： Heat Equation Boundary Condition Higher-Order Finite Difference Methods Hicks Approximation

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