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In the present manuscript, approximate solution for 1D heat conductionequation will be sought with the Septic Hermite Collocation Method (SHCM). Toachieve this goal, by means of the roots of both Chebyschev and Legendrepolinomials used at the inner collocation points, the pseudo code of thismethod is found out and applied using Matlab, one of the widely used symbolicprogramming platforms. Furthermore, to illustrate the accuracy andeffectiveness of this newly presented scheme, a comparison among analytical andnumerical values is investigated. It has been illustrated that this scheme isboth accurate and effective one and at the same time can be utilized in asuccessful way for finding out numerical solutions of several problems bothlinear and nonlinear.

A Robust Septic Hermite Collocation technique for Dirichlet Boundary Condition Heat Conduction Equation