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235 Abstract— This work deals with the computational techniques for solving initial boundary value problems in parabolic partial differential equations. The whole idea of the techniques is based on the replacement of the time derivative by the finite difference approximation and the space derivative by the cubic spline recursive relation. The resulting equations were than perturbed by Chebyshev polynomials which increased the number of unknown constants with extra computational efforts. Numerical examples are given to illustrate the effectiveness of the methods.

Application of Cubic Spline Collocation Method for the Numerical Solution of Parabolic Partial Differential Equations