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A wavelet-based collocation technique to find the discontinuous heat source in inverse heat conduction problems
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Abstract<p>This paper is devoted to an inverse problem of determining discontinuous space-wise dependent heat source in a linear parabolic equation from the measurements at the final moment. In the existing literature, a considerably accurate solution to the inverse problems with an unknown space-wise dependent heat source is impossible without introducing any type of regularization method but here we have to determine the unknown discontinuous space-wise dependent heat source accurately using the Haar wavelet collocation method (HWCM) without applying the regularization technique. This HWCM is based on finite-difference and Haar wavelets approximation to the inverse problem. In contrast to other numerical techniques, in HWCM, we used Haar functions that create a well-conditioned system of algebraic equations. The proposed method is stable and convergent because the numerical solution converges to the exact solution without observing any difficulty. Finally, some numerical examples are presented to verify the validity of the HWCM for different cases of the source term.</p>
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Publication Date
Mon Sep 20 2021
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Key Engineering Materials
Effect of Partial Substitution of Sr by Ba on the Structural Properties of Tl&lt;sub&gt;0.8&lt;/sub&gt;Ni&lt;sub&gt;0.2&lt;/sub&gt;Sr&lt;sub&gt;2-x&lt;/sub&gt;Br&lt;sub&gt;x&lt;/sub&gt;Ca&lt;sub&gt;2&lt;/sub&gt;Cu&lt;sub&gt;3&lt;/sub&gt;O&lt;sub&gt;9-δ&lt;/sub&gt; System
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In this manuscript, the effect of substituting strontium with barium on the structural properties of Tl0.8Ni0.2Sr2-xBrxCa2Cu3O9-δcompound with x= 0, 0.2, 0.4, have been studied. Samples were prepared using solid state reaction technique, suitable oxides alternatives of Pb2O3, CaO, BaO and CuO with 99.99% purity as raw materials and then mixed. They were prepared in the form of discs with a diameter of 1.5 cm and a thickness of (0.2-0.3) cm under pressures 7 tons / cm2, and the samples were sintered at a constant temperature o

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