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Numerical Heat Transfer, Part B: Fundamentals
An International Journal of Computation and Methodology
Volume 69, 2016 - Issue 4
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Original Articles

To recover heat source G(x) + H(t) by using the homogenized function and solving rectangular differencing equations

Chein-Shan LiuDepartment of Civil Engineering, National Taiwan University, Taipei, Taiwan, Republic of China;State Key Laboratory of Hydrology-Water Resources and Hydraulic Engineering, Center for Numerical Simulation Software in Engineering and Sciences, College of Mechanics and Materials, Hohai University, Nanjing, Jiangsu, People’s Republic of ChinaCorrespondence[email protected]
Pages 351-363 | Received 24 Jun 2015, Accepted 10 Sep 2015, Published online: 22 Mar 2016

Citations (16)

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Muhammad Ahsan, Iltaf Hussain & Masood Ahmad. (2022) A finite-difference and Haar wavelets hybrid collocation technique for non-linear inverse Cauchy problems. Applied Mathematics in Science and Engineering 30:1, pages 121-140.
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Chein-Shan Liu & Jiang-Ren Chang. (2021) A homogenization method to solve inverse Cauchy–Stefan problems for recovering non-smooth moving boundary, heat flux and initial value. Inverse Problems in Science and Engineering 29:13, pages 2772-2803.
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Chein-Shan Liu & Chih-Wen Chang. (2021) A spring-damping regularization of the Fourier sine series solution to the inverse Cauchy problem for a 3D sideways heat equation. Inverse Problems in Science and Engineering 29:2, pages 196-219.
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Chein-Shan Liu, Yung-Wei Chen & Jiang-Ren Chang. (2018) A regularized Fourier sine series solution of a 3D backward heat conduction problem with extremal long time span. Numerical Heat Transfer, Part B: Fundamentals 74:6, pages 807-817.
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Chein-Shan Liu & Dongjie Liu. (2017) Recovering a general space-time-dependent heat source by the coupled boundary integral equation method. Numerical Heat Transfer, Part B: Fundamentals 71:3, pages 283-297.
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Huan-Lin Zhou, Xing-Hang Zhao, Bo Yu, Hao-Long Chen & Zeng Meng. (2017) Firefly algorithm combined with Newton method to identify boundary conditions for transient heat conduction problems. Numerical Heat Transfer, Part B: Fundamentals 71:3, pages 253-269.
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Articles from other publishers (10)

Chein‐Shan Liu & Lin Qiu. (2022) Solving the 2D and 3D nonlinear inverse source problems of elliptic type partial differential equations by a homogenization function method . Numerical Methods for Partial Differential Equations 39:2, pages 1287-1298.
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Ji Lin & Chein-Shan Liu. (2021) Recovering temperature-dependent heat conductivity in 2D and 3D domains with homogenization functions as the bases. Engineering with Computers 38:S3, pages 2349-2363.
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Chih-Wen Chang. (2022) Solving Cauchy Issues of Highly Nonlinear Elliptic Equations Using a Meshless Method. Computers, Materials & Continua 72:2, pages 3231-3245.
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Chein-Shan Liu & Chih-Wen Chang. (2020) Reducing the near boundary errors of nonhomogeneous heat equations by boundary consistent methods. IMA Journal of Applied Mathematics.
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Chein-Shan Liu, Lin Qiu & Ji Lin. (2019) Solving the higher-dimensional nonlinear inverse heat source problems by the superposition of homogenization functions method. International Journal of Heat and Mass Transfer 141, pages 651-657.
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Chein-Shan Liu, Yung-Wei Chen & Jiang-Ren Chang. (2019) Solving a nonlinear convection-diffusion equation with source and moving boundary both unknown by a family of homogenization functions. International Journal of Heat and Mass Transfer 138, pages 25-31.
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Chein-Shan Liu & Chih-Wen Chang. (2019) Solving the 3D Cauchy problems of nonlinear elliptic equations by the superposition of a family of 3D homogenization functions. Engineering Analysis with Boundary Elements 105, pages 122-128.
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Chein-Shan Liu, Lin Qiu & Fajie Wang. (2019) Nonlinear wave inverse source problem solved by a method of -order homogenization functions . Applied Mathematics Letters 91, pages 90-96.
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Chein-Shan Liu. (2016) Homogenized functions to recover / by solving a small scale linear system of differencing equations . International Journal of Heat and Mass Transfer 101, pages 1103-1110.
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Chein-Shan Liu. (2016) An integral equation method to recover non-additive and non-separable heat source without initial temperature. International Journal of Heat and Mass Transfer 97, pages 943-953.
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