Visual Analysis of the Exact Solution of a Heat Equation
Himanshu Agarwal
Himanshu Agarwal, Department of Mathematics, Jaypee Institute of Information Technology, Noida (Uttar Pradesh), India.
Manuscript received on 29 June 2019 | Revised Manuscript received on 05 July 2019 | Manuscript published on 30 July 2019 | PP: 1968-1973 | Volume-8 Issue-9, July 2019 | Retrieval Number: I8576078919/19©BEIESP | DOI: 10.35940/ijitee.I8576.078919
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© The Authors. Blue Eyes Intelligence Engineering and Sciences Publication (BEIESP). This is an open access article under the CC-BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/)
Abstract: The solution of the two-dimensional heat equation is represented as images. The images provide quick but approximate insights to the solution. Approximation by image visualization depends on many factors such as the display device, human eye factors, image resolution (sampling rate and bit depth of the image), and image resize methods. We have provided images for different time t and different resolutions We have studied the impact of different sampling rate and different image resize methods on the quality of the images. User study is performed for qualitative inspection and peak signal to noise ratio (PSNR) is used as a quantitative measure of the relative similarity in images with respect to different sampling rate and time t . Qualitative inspection and PSNR follow the same trend. Further, Qualitative inspection confirms that the quality of approximation of solution by image visualization improves with increase in sampling rate. Moreover, lanczos3 is the best interpolation method to resize the images.
Keywords: Heat Equation, Boundary Condition, Initial Condition, Visualization, Pixel, PSNR
Scope of the Article: Analysis of Algorithms and Computational Complexity