Existence of the unsteady heat conduction in Sobolev space and numerical technique with twenty-one global nodes

What is it about?

We are interested in the existence of unsteady heat conduction in Sobolev space by using the Littlewood-Paley decomposition and also Gronwall inequality to establish the uniqueness of the solution. We further consider one- dimensional unsteady-state heat conduction to make an easy numerical technique. Furthermore, this Equation is discretized as 20 subdomains to obtain 20 elements and 21 nodes called global nodes. Every global node consists of element nodes having the same basis function for all element nodes. These all element nodes will be assembled to be a global stiffness matrix with 21 unknown temperature values for each iteration of time. The homotopy perturbation method is then used to approximate the analytic solution to one-dimensional unsteady heat conduction.

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